Here are your parts
Replacement parts for WHIRLPOOL REX6634PQ0 | AppliancePartsPros.com

Here is the wiring diagram
http://www.servicematters.com/d...0Sheet%20-%208528187.pdf

thermostat or thermal cut off bad?
Will not be the thermal cutoff as this is like a fuse so if it blows, it has to be replaced.

Could be the operating thermostat.

If you have no control over the heat it could be a grounded element re: the element has sagged or broken and is touching the case.
Unplug the unit.
Disconnect both wires going to the element.
Measure the element, should be around 10 ohms.
Then measure from each heater connector to the case/frame, both should be open (infinite ohms)
Sometimes you can see the problem by inspecting the element.

Also may just be that your vent system is dirty or the outside louvers are not opening.
Vent Check
Undo the dryer from the exhaust
Run a load
If the load dries correctly then you have a vent problem.
Clean/check the vent system. Make sure the outside louvers open fully.

If you do not want lint in the house.
Take a pair of pantyhose, put one leg into the other and attach this to the dryer exhaust.
Leave enough room behind the dryer so it can blow out like a windsock.
Run a load.

Both the above will allow you to check the air flow and temp.