Here are your parts
Replacement parts for WHIRLPOOL REX5634KQ1 | AppliancePartsPros.com

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

I am assuming from your description that you are getting some heat but the unit is cycling too often.

[COLOR="Blue"]I'm having a problem with my dryer getting hot but it seems not hot enough to dry the clothes. If I run it for two or three cycles the clothes will finally get dry.[/COLOR]
The most common cause of this is a clogged vent system so I would try the following first. Also clean/check the blower wheel.
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.
Also the above is NOT recommended for a gas dryer due to possible carbon monoxide problems.
[COLOR="Blue"]
The heating element is good.[/COLOR]
How do you know this, did you measure it with a meter?
Sometimes an element will ground and cause low heat.
Check the heating coil.
Unplug the unit and both wires to the coil.
Check it with a meter, should be around 10 ohms.
Then check from each side of the coil to the case/frame, both should be infinite ohms (open). If not the coil may have sagged or broken and is touching the case (grounded).

[COLOR="Blue"]I am guessing it is a cycling thermostat but just not sure. I am thinking this dryer has three thermostats and have found two of them but not sure were the other is.[/COLOR]
The hi-limit thermostat and the heater's thermal cutoff (fuse) are on the heater assembly. The operating thermostat and the motor's thermal fuse are on the blower assembly. See Section 3.

[COLOR="Blue"]Is there a way I can test the thermostat to see if it is ok?[/COLOR]
The normal way for them to blow is either their contacts weld together or the blow open. There is really not a reliable way to check at what temperature they are opening.

[COLOR="Blue"]Wondering if my cleaning making sure the connections were good corrected the problem or is something really going out and my moving it caused it to work?[/COLOR]

Cannot say why it started up OK.
In any case you will have to wait and see if it fails again.