Cold water connection is hot

Broken solder connection.
Continual expansion and contraction of metal due to hot and cold extremes will cause metal fatigue. The most vulnerable place is at the join. Other places can fail, but usually the solder join will fail first.
Buy another one and support economy.
Make sure next unit is connected to cold water line, and not hot water line. If hot water dispenser is connected to Hot line, then it will cause water heater to run each time water is drawn through dispenser because cold water immediately enters tank.
http://waterheatertimer.org/Water-heater-dip-tube.html
http://waterheatertimer.org/How-to-install-under-counter-water-heater.html#h-c
http://waterheatertimer.org/9-ways-to-save-with-water-heater.html#pot
You might also consider installing small tank under counter. Tanks are less glamorous than hot water dispensers but tanks are more reliable long term than instantaneous water heaters.

If you need further help, I’m available over the phone at https://www.6ya.com/expert/gene_9f0ef4df2f9897e7

large water heater, turn p the themo stat to a higher setting ( watch for burns with young childern and older folks)

or the best install a tempering valve. this valve mixs hot water with cold water before it goes into the building.

Again if you have young ones or old people they can burn faster than any other group.the best is a larger heater for the DIY person.

Thanks Tom

If I understand correctly you have residential electric water heater, and your shut off valve located above water heater on cold-water line is leaking?

1) Hot water would come out of this valve if it's leaking because water inside tank is hot and under pressure ... also remember, hot water rises so tank is probably heating the water inside the cold line during hours when no hot water is being used.

2) You probably need to replace the valve. But if water is leaking because a pipe is rusted, the valve may be ok, and just the pipe needs to be replaced.
Take a photo of your problem to hardware store or home center.
I used to work in those stores and could help folks get the right parts.

3) Here are some steps for replacing the valve.
Shut off main water source into house. This is usually located underground in same box where meter-reader looks at meter.
Your water heater shut off valve is called a gate valve, and it will be 3/4"
All water heater pipes are 3/4"
You will need two 10-12" pipe wrenches, maybe a new gate valve, maybe a new flex connector, probably short 3/4 pipe pieces, teflon tape for each threaded pipe.
Hardware store or home center can get you the right materials, just take a photo over to hardware store

4) When you get started, turn off water heater circuit breaker for a couple hours so water will cool down. You don't want to get scalded with hot water.
Do NOT drain the tank.
Simply open a bathtub faucet on hot side to release pressure.
When finished, turn on the water, and make sure water is flowing out of tub spout in full stream before turning circuit breaker ON

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 tank is rusted out and needs to be replaced.
Link below is a troubleshoot for leaking water heater.
http://waterheatertimer.org/Leaking-water-heater.html

Protect yourself first:
If your tank is rusted, there is danger of rupture.
My friend welded his leaking tank, but he assumes the risk.
Ruptured tank can cause massive damage and water runs until it is shut off.

Hot water tank is under pressure because hot water expands and pushes against tank wall.
Turn off water to tank.
Turn off power supply:
Electric: turn off circuit breaker.
Gas: rotate knob to pilot so pilot stays lit but burner will not fire. To turn back on, rotate knob to ON.
Open hot side bathtub valve and relieve pressure on tank.

You can limp by with rusted tank by turning water heater on when hot water is needed.
Shower uses 5-9 gallons hot water
Bath uses 12-15 gallon hot water
Ordinary gas heater makes 41 gallons hot water per hour
Ordinary electric heater makes 20 gallons hot water per hour.

I buy water heaters at Lowes, Home Depot, Ace.
Look for scratch and dent models.
Buy drip pan for water heater.
Wrap electric heater totally with insulation except TP valve.
Buy new flexible connectors for water lines.
Offer 15% less than marked price on tank, because the store makes money on additional items.

> Most people can install their own electric heater since you just connect water pipes and electric wire, and it's done. Read link below since there are tips that help you buy and install electric.
> Generally people are nervous about installing gas water heater, so step-by-step instructions are shown on link below. Remember gas line is under less pressure than water line, so if you can install a water pipe, you can install gas line to water heater with crescent wrench, and soapy water to check for leaks.
How to install gas water heater:
http://waterheatertimer.org/How-to-install-gas-water-heater.html

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

You have 240volt electric water heater
Check both elements for leaking.
Check top of tank for leaking pipes.

If water heater is leaking from side of tank, then tank is rusted out and could rupture.
This tank must be replaced.
http://waterheatertimer.org/Water-at-bottom-of-water-heater.html
My friend welded his tank to get more life out of tank, but he assumed the risk.

Hot water heaters are under pressure from heated water which expands.
If tank ruptures, water will flood out of tank and water will run until shut-off is turned OFF.
This causes major damage inside home.

Protect yourself first, and then let's talk more.
1) Turn off water at shut off located on cold water line above tank.
2) Turn off power to water heater:
Gas heater, rotate valve to 'pilot' so pilot is lit but burner does not turn ON.
Electric heater, turn off circuit breaker.
3) Open tub spout on hot side and let run a bit to relieve pressure.
4) Now your property is safe.

You can limp along with failed heater if leak is slow.
Turn heater ON when you need hot water.
Typical Gas heater makes 41 gallons hot water per hour.
Typical Electric heater makes 21 gallons hot water.
Shower uses 5-9 gallons hot water, bath uses 12-14 gallons hot water.
http://waterheatertimer.org/images/Water-heater-reference-guide-2.jpg

If you are going to install heater yourself:
Look at label on side of old tank to identify size and particulars.
I buy ordinary heaters from Lowes and Home Depot and always buy scratch-n-dent models when possible, because superficial damage to outer tank does not lower lifespan of heaters I have installed.
Buy same size heater if it worked fine before.
Buy new flexible water connectors.
Set water heater in drip pan.
Offer 10% less than price shown. Make them deal with you. Shop Ace hardware, Lowes, Home Depot. Kick the tires since you have a bit of time.

I know you have electric heater, but many folks read these answers, so I include info on gas too.
#1 rule) tankless heaters are a rich-man's toy, because tankless will never pay you back, and will become major money pit if you encounter 1 repair. Electric tankless heaters require larger electric service box. Gas tankless require larger gas line (larger gas line, more gas consumption, bigger bill unless you cut consumption)
2) How to install gas heater:
http://waterheatertimer.org/How-to-replace-gas-water-heater.html
3) How to install electric heater:
Read link above because many of same steps apply to electric.
The difference with electric, is turn off power, disconnect wires, and reconnect wires exactly like before. Set electric heater directly on insulated surface like dense blue styrafoam. Cut styrafoam in circle so it fits inside dip pan. Wrap entire electric heater with insulation blanket, except don't cover TP valve.
4) Connect bare copper jumper wire between hot and cold pipes to prevent stray current corrosion which will shorten life of tank. Make sure cold water line is grounded.

Also read:
http://waterheatertimer.org/9-ways-to-save-with-water-heater.html

Add a comment for more free assistance.
Also take advantage of fixya phone service.
For a price, fixya expert speaks to you via phone about any do-it-yourself problem.

You have clog in the water line.
Since all hot water pipes are involved, clog is probably near water heater.

Buy pressure gauge at hardware store that threads onto hose connection.
Brady BTG 100 at Amazon
Picture of gauge

Check outdoor pressure for baseline pressure in your home.
Turn off electricity to hot water heater for an hour or two so there is not scalding water.
Open drain valve on water heater to see if water heater is clogged with sediment.
http://waterheatertimer.org/Water-heater-will-not-drain.html

Put pressure gauge on drain valve and compare with outside pressure.
Open hot water spigot on bathtub and see if tank pressure drops ... if tank pressure drops significantly with bathtub spigot on, then clog is on incoming cold water before tank, and could be on outgoing hot water pipes too.
If tank pressure stays about the same, then clog is on outgoing hot water pipes.

Clog can be sediment caught in cold water shut off valve located above tank. Open and close valve and test pressure again. Take apart incoming cold water pipes above tank and check for sediment. Replace valve. Look at condition of cold water nipple on top of tank.

Sediment caught at hot water elbow near tank.
Sediment can fill up old pipes. Take apart hot water pipes above water heater and see condition.
Look at condition of hot water nipple on top of tank.
You may have to take apart pipes up to first or second elbow.

Pipes can decay at joint where copper pipe connects to galvanized pipe. Check for copper to galvanized connections on cold or hot pipes and replace section of galvanized pipe. Copper pipe will probably be good, the galvanized pipe will deteriorate. Replace copper-to-galvanized joint with 3/4" non-conducting union from hardware store

How big is your bathtub? Is your water heater set on the hottest setting? What is the temperature of the hot water at the tap?

Keep in mind that hot water can cause severe burns. Children and those with diminished mental capacity can be seriously harmed by hot water.

The "40 Gallon" rating on the water heater is usually the amount of hot water the unit can produce in one hour. So the tank, and the amount of immediately available hot water, might be smaller than 40 gallons.

My bathtub is 2 feet wide by 1 foot deep and 4 feet long. This is 8 cubic feet or almost 60 gallons. So a 40 gallons of water at 120 degrees, mixed with 20 gallons of cold water (60 degrees), fills the tub with 100 degree water. My January cold water is 42 degrees, so it will take 40 gallons at 129 degrees to fill the tub. If the tub is cold to start it will take even hotter water.

So the water heater might be just fine.

Possible solutions:
1. turn the temperature up on your water heater- or the temperature control could be malfunctioning and not getting the water hot enough.
2. insulate your hot water pipes so that the water loses less heat on the way to the tub.
3. bigger water heater.
4. smaller bathtub, or less full bathtub.

If it is a new water heater it might be that the water supplies are crossed. The cold water should be installed on the right hand side of the tank or on the bottom if your tank hooks up on the side. If its an older water heater the dip tube may have broken off. This is a tube that runs from the top of your water heater on the cold side to the lower portion of the tank.It puts the cold water in the bottom of the heater which pushes the hot water to the top.To change the dip tube out you must disconnect the cold water supply from the 3/4 inch nipple at the top of the tank. Then with a pipe wrench unscrew the nipple from the tank it will have the remainder of the tube on it.You can get a replacement dip tube at a plumming supply. Installation is opposite of removal. If this is your problem I suggest you get a new water heater .Usually its caused from minnerals in the water or buy two dissimiler metals being connected together in the water piping system causing corrosion Your water heater will probably fail in the near future.

Most electric water heaters have 2 heaters - an upper and a lower, each with it's own thermostat. These are readily accessible by removing the screw covers on the side of the tank. Careful - the thermostats have 240VAC on the terminal screws (unless you have a small 120VAC heater) if the circuit breaker or fuses feeding the heater are still on - turn them off before proceeding. After removing the two screw covers and pulling back the insulation you will see temperature (screw) adjustments for the upper and lower thermostats, with a temperature indicating pointer attached to each screw. Set both thermostats to 125 degrees or so. Push the insulation back in place, replace the covers and turn the circuit breaker back on that feeds the water heater. You should have warm water within 15 minutes and hot water within a hour or so.

If the water still does not heat, then you have to troubleshoot to find the problem. With a voltmeter determine if 240VAC is actually getting to the water heater. Remember, the upper element has priority over the lower element, and if the water is cold, the upper element will try to turn on and this locks out the lower element (only one element is allowed to heat at any given time). The lower element comes on ONLY after the upper thermostat is satisfied. Therefore if the upper heating element is burned out you will never get any hot water. If you suspect this, TURN OFF THE POWER TO THE HEATER and take a resistance check of the upper element.