How do I wire around upper heating element until I can get an other one to replace it?

I should like to hope I have your answer.
If yours is like most U.S. model, it is called a 220 volt unit.
That is not really 220 volts, it is really 2 separate 110 volt units.
What that means is, there are actually 2 separate 110 volt hot wires to the water heater, usually one hot wire is black, and the other hot wire is red.
One is for the upper heating unit, one is for the lower heating unit. Perhaps your lower unit has blown the circuit breaker for that line.
I mean the circuit breaker in the main fuse box/circuit breaker box.
Did you test the lower wiring to see if the hot wire is hot?
If it is hot, be sure to test the ground wire, and also the wiring between the bottom and the top of the heater inside it.
God bless your efforts.

Short answer: Thermostats may be bad. Replace both thermostats.
http://waterheatertimer.org/How-to-replace-thermostat-on-electric-water-heater.html

Long answer:
1) If water heater has some hot water, then upper element is good and water heater has 240Volts, and best suspect is burned out lower element.
http://waterheatertimer.org/How-to-clean-sediment-out-of-electric-water-heater.html

2) If water heater has no hot water because 240volt circuit breaker is tripped on one leg, and only 120Volts is arriving at water heater, then upper part of water heater can appear to have voltage and lower part of water heater can appear to have no voltage.
Open following links for troubleshoot steps:
http://waterheatertimer.org/How-to-troubleshoot-electric-problems-with-water-heater.html
http://waterheatertimer.org/Test-electricity-to-water-heater.html

Add a comment for more help

1) Residential water heaters are non-simultaneous. Only one element works at a time.
Upper element comes on until top of tank is heated, and then lower element is switched on until lower part of tank is heated. Lower element keeps tank hot during standby hours
http://waterheatertimer.org/How-it-works.html

2) Typical Whirlpool energy smart has 4500Watt elements. Look at label on side of tank
If both elements were ON, that would draw 9000Watts or 37.5 amps, requiring 50 amp breaker and 8 gauge wire. V x A = Watts.
All dual-element tanks are 240V.
Whirlpool energy smart requires 10 gauge wire and 30 amp breaker so electronics are not starved during operation. If your wire or breaker are undersized, that is suspect for repeated failure.
http://waterheatertimer.org/Whirlpool-Energy-Smart-electric.html

3) Typical electric water heater heats 21 gallons per hour. First hour delivery is higher since elements heat water as you use it. Overall however, electric water heater cannot re-heat as fast as gas because gas water heater burner carries more BTU punch per minute than electric element. Gas heats about 41 gallons per minute, with higher first hour delivery.

4) IF YOU HAVE OLDER energy smart and installed newer board, then you could have non-simultaneous operation is reversed so that lower element comes on first.
Read following post at Fixya:
http://www.fixya.com/support/t8263226-our_water_heater_doing
Contact Whirlpool 1-877-817-6750

5) Another potential problem is that you have sediment inside tank and that is reducing efficiency of lower element.
http://waterheatertimer.org/Clean-sediment-out-of-water-heater.html
http://waterheatertimer.org/How-to-test-water-heater-element.html

Add a comment with your experience so others with same-similar problem can benefit.

Also take advantage of fixya expert assistance live.
For a price, expert works with you while you work on water heater or any do-it-yourself project.
Fixya is always less expensive than a service call.

Electric water heaters never power BOTH the upper and lower elements at the same time.

If the water in the tank is cold, either the top OR bottom element will be powered through the upper thermostat (t-stat), never both at the same time. The upper t-stat will send power to the upper element until the temperature of the water in the top of the tank reaches the set point of the t-stat say 140 degrees. When the water temperature in the top of the tank reaches 140 degrees, the t-stat is "satisfied" and disconnects the power from the top element and sends it to the lower t-stat.

IF the temperature of the water in the lower half of the tank is lower than the set point of the lower t-stat, the t-stat closes to send power to the lower element. The lower element REMAINS powered by the t-stat until EITHER the water in the lower part of the tank reaches the set point temperature of the lower t-stat again, say 140 degrees; OR the temperature of the water in the upper part of the tank drops, at which point the upper t-stat "calls" and switches the power away from the lower t-stat and sends it to the upper heating element instead. When the top t-stat is satisfied, it switches power back to the lower t-stat. The process will continue back and forth for as long as needed to bring the temperature of the water in both halves of the tank to 140 degrees.

You must wait until the top of the tank is heated - before the lower element will be powered to heat the water.

I hope this helps you understand how the switching happens in these water heaters. Good luck! Please rate my reply. Thank you.

Reset trips when upper thermostat senses high heat event over 150 degrees F.

High heat can be caused by:

1) Element shorted to ground through center of element. Thermostats turn off one leg of 240V circuit. Elements always have 120V available. If element is shorted to ground, it might not trip breaker, and continues to heat using one leg of 240 with circuit completed to ground wire.
Test elements:
http://waterheatertimer.org/How-to-test-water-heater-element.html
http://waterheatertimer.org/How-to-wire-EH40-hot-water-heater-timer.html#120-240

2) Insulation and cover not put back over thermostat. Thermostat exposed to cool air, misreads temperature causing element to continue heating.

3) Thermostat sticking in ON position. I usually replace both thermostats at same time to save another trip.
http://waterheatertimer.org/How-to-replace-thermostat-on-electric-water-heater.html

4) Shorted wire or loose wire at or near upper thermostat. Check that screws are very tight against copper wire.
http://waterheatertimer.org/How-to-troubleshoot-electric-problems-with-water-heater.html

5) One suspect can be eliminated is 240Volt power to heater.
Your heater circuit is good.

Add a comment for more free help.
Also take advantage of fixya phone service.
For a price, expert speaks with you over phone while you work on water heater or any do-it-yourself project.
Fixya is always less expensive than a service call.

Your water heater has 2 elements so its 240Volts.

1) If breaker is delivering power on one leg of the 240Volt circuit, then water heater can appear to have electricity, but tank is receiving 120V. Both 120Volt legs are needed to complete the 240V circuit. Double check for 240Volts.

2) Review electric Load.
Water heater label shows wattage of tank.
If tank is 4500Watts for example, you installed 3500 or 4500 watt elements.
With 5500 Watt elements you need 30 amp breaker and orange-colored 10 gauge wire
With 4500 Watt elements you can get by on 20 amp breaker and 12 gauge wire up to 75 feet away.

3) Check ECO red reset button on upper thermostat. If reset is tripped, then ECO is reading high temperatures. Suspects at this point are defective upper thermostat, shorted wire or bad lower element.

4) Also note that insulation and cover must be re-installed over thermostat. Thermostat reads temperature through wall of tank. If outside air circulates around thermostat, that can cause a mis-read and cause tank to overheat and ECO trips.

If you don't want to test the heater, replace both thermostats for about $25. Return the upper thermostat for a refund. Then see of problem persists.

Here's what I would do.
1. Check breaker for 240
2. Check water heater for 240 across 1 and 3 screws on upper thermostat
3. Note wiring and breaker size.
4. Note label on side of tank.

5. Look at end of new element to see wattage printed on each element. Look for sings of high heat and burning. Tighten screws on elements.

6. Check ECO reset button. Look for high-heat and burning. Tighten screws on thermostat.

7. Test upper thermostat as follows:
http://waterheatertimer.org/images/Electric-diagram-water-800.jpg
Test left-side #1 screw to right-side middle #4 screw. Test should read 240V at all times. If not, then ECO is tripped, thermostat is bad, or electricity is OFF

8) Water heater is cold so upper element should be ON. Test upper thermostat.
Test right-side #3 screw to left-side bottom #2 screw and it should read 240V
Test right-side #3 screw to right-side bottom #4 screw and it should read 0 volts

8. If upper thermostat checks out. Test upper element for 240 across both screws. If upper element does not read 240 when water is cold, then element is bad or there is a shorted wire between element and upper thermostat.
How to test element:
http://waterheatertimer.org/How-to-test-water-heater-element.html

9. Do a full troubleshoot on electric water heater
http://waterheatertimer.org/How-to-troubleshoot-electric-problems-with-water-heater.html

http://www.rheem.com/product.aspx?id=09DF2BDD-5E11-4D32-B574-84ACFB8A4619
http://globalimageserver.com/fetchDocument.aspx?id=052c9e32-ce37-48d7-8990-9e430f23fef3

82V80-2 Energy factor is .86 according to water heater industry self-regulated standards.

Rheem pdf says these water heaters are wired for non-simultaneous operation.
Except special order water heaters.
Non-simultaneous operation uses single 240V circuit as described below.
If your water heater is wired for simultaneous operation, and each element is on a separate circuit, that makes your water heater special order. I would guess the reason is for higher first-hour delivery, which implies rapid heating and would likely affect energy factor.
You might want to get serial number off model and call Rheem for specs on that special order.

Your water heater energy factor may be the same because 'energy efficiency is based on the amount of hot water produced per unit of fuel consumed over a typical day.' This means an aircraft carrier can be considered highly efficient despite overall cost. And naturally the guys making the aircraft carrier are also doing the rating.
http://www.energysavers.gov/your_home/water_heating/index.cfm/mytopic=13000

Non simultaneous operation means the upper thermostat controls heating functions.
240V goes to upper thermostat first.
When water inside tank is cold, thermostat reads temperature through tank wall.
Upper thermostat turns on upper element until top 2/3 of tank reaches thermostat set point.
Once set point is reached, upper thermostat turns off upper element and sends power to lower thermostat and lower element.
Lower thermostat reads temperature through tank wall, and turns on lower element until bottom 1/3 of tank reaches thermostat set point.
As water cools inside tank, lower thermostat is first to respond since hot water rises.
Lower thermostat turns on lower element until tank again reaches set point.
When hot water faucet is turned on, hot water exits top of tank.
At same time, cold water enters bottom of tank through the dip tube.
The heating cycle repeats.
At all times, the electricity flows through upper thermostat. And upper thermostat is powered by one 240V circuit.

With simultaneous operation, the upper and lower thermostats work in same manner.
Except thermostats are wired separately.
Lower thermostat does not wait for upper part of tank to be heated first.
Lower thermostat turns on whenever lower part of tank cools.
The advantage is more hot water available rapidly when demand is high. This is called first hour recovery.

One method for reducing electric consumption is to set lower thermostat so it only turns on during certain times of day. For example Whirlpool Energy Smart operates in this manner and shaves a few bucks off the bill each month. This says that simultaneous operation is not an energy saver, unless that circuit controlling lower thermostat is set on a timer.

You can open the top up again. I would not turn the temp higher than 130 degrees, maximum. However, there should be above the thermostat a red button. This is where the power wires connect to the thermostats and heating elements. Sometimes this button needs to be reset, press it and discern if you hear a click sound. This means that the high temperature safety switch has tripped open and you had to manually "reset" it. There are two thermostats by the way. The water heater usually works this way. There are two thermostats and two heaters. The upper tank heater turns on first and it heats the top half of the tank. Then when the thermostat above is satisfied it then allows the bottom heater to come on and heat the bottom half of the tank. You might want to set the bottom heater thermostat as well. This is made this way because it is actually faster and more efficient to heat the top half first and the bottom half secondly. Try this first with the reset button. We could check voltages, but that requires a level of knowledge and safety that I am not sure that you are comfortable with. Pictures of the upper and lower thermostats and connections will help if the "reset" does not do the trick. By the way, not meaning or implying anything, but did you move the thermostat in the right direction? Sometimes the dials can be confusing.

Electric water heater can be repaired by homeowner
If I understand correctly, water heater is producing no hot water.
Reset button clicks in, but still no heat.

Three initial things can be causing this:
1) No power to water heater. Test across top two screws on upper thermostat for 240V. Red and black wire are attached to these screws. Screws are marked 1 and 3. Upper thermostat is same that has reset button. If power tests 120 across screws, then breaker may be off on one leg. If no power, then start testing at breaker.
http://waterheatertimer.org/How-to-troubleshoot-electric-problems-with-water-heater.html

2) Upper thermostat is bad. Replace thermostat with generic upper thermostat available at hardware store.
http://waterheatertimer.org/How-to-replace-thermostat-on-electric-water-heater.html

3) Upper element is bad. Test and replace element using Rheem 4500 watt element available at hardware store. Image shown below. Look at label on side of tank for element wattage. Rheem puts 4500 watt elements into all their 240V electric water heaters.
http://waterheatertimer.org/How-to-test-water-heater-element.html

If upper element is burned out the tank will not heat any water.
http://waterheatertimer.org/How-it-works.html

Rheem 4500Watt element


Upper thermostats are generic and interchangeable:

The reset button kicks out because the thermostat detects overheating.
Anything over 150 degrees, the reset kicks out.

This is caused by 4 things.
1) Bad upper or lower thermostat. Thermostat sticking in 'on' position and elements overheating water.
2) Factory-installed insulation and cover are removed
3) Bad element shorted to ground at center of element, and element continues heating with 120V through the ground wire.
4) Loose wire near upper thermostat, that is shorting and causing heat.
http://waterheatertimer.org/How-to-troubleshoot-electric-problems-with-water-heater.html

Solution:
Check for missing insulation.
Check for loose and burned wires.
Replace both upper and lower thermostat.
http://waterheatertimer.org/How-to-replace-thermostat-on-electric-water-heater.html

If problems continue, test water heater elements and replace bad element.
http://waterheatertimer.org/How-to-test-water-heater-element.html

If you need more help, add a comment and I will respond.