Short answer: The cycling thermostat is behind the rear panel of the dryer on the left. The hi-limit thermostat is on the element housing on the right at the bottom.
Detailed instructions including common and expensive mistakes:
Unplug the dryer from the wall
Disconnect the transition duct (the flex duct that connects the dryer to the dryer vent)
There will be 9 different 1/4" hex cap screws around the perimeter. Take the screw out that holds the terminal block cover first (where the cord connects to the dryer, it's on the right) and set aside.
I usually take out the top screws last so the panel doesn't fall on me.
With the screws out, gently lift the dryer cord up so you can remove the panel.
The operating or cycling thermostat is held onto the blower housing assembly on the left. It will have 4 wires connected to it. In my experience, these are very rarely at fault. Part no. 3387134 Picture:
Next is the thermal fuse. If the thermal fuse fails, it means the outlet temp of your dryer was over 195F or so indicating a primary fault (the fuse being the secondary fault). To test, disconnect the wires from the terminals. Connect two leads of an ohmmeter or a multimeter set to ohms (Rx1 or Rx10 if it isn't auto-ranging) to the exposed terminals. It should read less than 1 ohm (0.2-0.6ohms is common with most meters.) If it reads infinite or if it's digital and reads 1, the fuse needs to be replaced. Do not replace it until you determine what caused the overheating initially. Part no. 3392519 Picture:
On the right hand side, you will find the thermal limiter and hi-limit thermostat. The thermal limiter acts in a similar manner to the thermal fuse but at much higher temperatures. It is located at the top of the element housing and duct. Testing is the same as for the thermal fuse, and if this is the culprit, it should be treated as a secondary failure.
Thermal limiter picture:
The hi-limit, like the operating or cycling thermostat, rarely ever fails. Typically a failed thermal limiter is the result of too large of a load in the dryer or improper ventilation. Testing is the same as for the other components. Because Whirlpool has to assume that the hi-limit should have de-energized the circuit to the heater BEFORE the thermal limiter failed (it cycles at a lower temperature), these two items now come in the same bag. If you decide you want to replace both at the same time (and it's recommended that you do), you will need to gently pry the brass (sometimes silver-plated) terminal connector seen in the top right corner below. Part no. 279816 Picture:
A couple of notes on ventilation (READ THIS)
If the dryer is heating at ALL and I mean if there's just the faintest bit of heat, the problem isn't in your dryer, it's in the ventilation. If your dryer is located in an interior room, you need to visually verify that the dryer duct is made from smooth walled 4" circular aluminum or galvanized pipe. 3" won't work, and flex duct in any enclosed area like in a wall or under the floor (it's fine behind the dryer, as long as it isn't kinked or excessively long) has been a building code violation since 1974. Unfortunately that doesn't count for much because I routinely find flex duct where it doesn't belong in brand new construction. Happens all the time, take my word for it. Also, check that the termination of the duct (the cap) isn't clogged and doesn't have a mesh or screen on it.
A. The dryer will start, with the motor spinning and drum turning but there is no heat
1. Turn the breaker for the dryer off and back on.Remove terminal block cover (1 screw). Plug in the dryer. Measure the voltage from the middle wire (just touch the back of the screw) to the each side wire. You should get 120 volts AC. Then measuring the outside two, you should get 240v. If you get 0 here, or if you get a value that isn't close to any of those (10-100v), you need to call an electrician. If OK, continue.
2. Check the thermal limiter. If failed, replace.
3. Check the element (two 5/16" terminals at the base of the duct on the right hand side). It should read 10-30 ohms with your meter set to Rx100 or whatever setting it has that's larger than the value you anticipate. Also check ohms between each terminal of the element to the metal housing around the element. These should both read infinite resistance. Check this with the HIGHEST ohms value available to you. Don't touch the metal ends of the probes, as the meter may read resistance through your skin. If failed, replace. Part number is 279838.
4. Check the operating thermostat (across the two big terminals on the outside, no need to check the smaller two which power a tiny heater) and hi-limit thermostat. These should read less than 1 ohm at room temperature. If either has failed, replace.
5. If all of this checks out and your dryer isn't heating at all, you probably have a failed drive motor. If you can do the repair yourself, buy a motor. If you have to pay a servicer, it's more cost effective to replace the dryer altogether.
B. If the dryer won't start at all
1.Verify proper voltage (see above)
2. Check that the door switch is being depressed. It will be behind the closing surface of the door, usually at the top. They're usually ok if you depress the switch and hear or feel a sharp little click. With the dryer still plugged in, turn the timer to a timed cycle, say 40 minutes. With the door closed, put your ear next to the timer knob. If you can hear the timer motor moving or the timer moves down over a course of 30 minutes, the door switch is ok.
3. If you can't hear the timer motor moving and the door switch is in good shape and clicks when you press it, disconnect the power from the dryer and proceed to check the thermal fuse on the left.
4. If the thermal fuse is good, there are a few things that could be the issue. I won't go into disassembly instructions, so you may need to call a technician.
a. Failed door switch. Should read less than 1 ohm when depressed.
b. Burnt wiring, especially at the terminal block.
c. Similar to "b", but the neutral circuit is broken or burned somewhere. This is uncommon.
If you skip any of these steps, you're going to be doing more work than you need to, and you may be throwing money away on a service call or repeat parts failures.