Sounds like you have had a rough ride.
I would say that your current problem is from the heater relay contacts always being closed. This could be that they are welded together or that the relay control circuitry is bad.
Shouldn't the thermostats open when it gets to a certain temperature?
I am assuming that the thermostats you are referring to are on the heater. One is a high limit thermostat and the other is a thermal cut-off (fuse).
They are both safety devices and only come into play if there is a problem in the unit.
So lets say hat for some reason the heater temperature becomes too high, then the high limit contacts open. It's contacts are not that robust so after a while of opening and closing they fail (usually short together)
The thermal cut-off is a secondary safety so then it blows killing power to the heater.
Also, in an effort to help you understand the problem... the over heating problem occurs on any heat setting... high heat, low heat, even when I run it on no heat "air only" setting. Any ideas on this?
That you get heat on an air only cycle is what leads me to believe that it is a heat relay problem.
One way to check if the contacts is to unplug the unit and the wires to the heater relay and then measure across the contacts. It should be infinite ohms (open).
If it is zero or low ohms then the relay contacts are welded together.
Note this does not rule out the relay control circuitry.
I know that it's a reach, but is it possible that the thermostats are not sensing the correct temperature since I have the bottom panel off the dryer?
Having just the bottom panel off should not have an effect as long as all cowlings, seals etc. in the air flow path are OK.
Also the thermistor is the only real temperature sensing device all other thermostats are safety devices.
Below is a link to a GEW9200 service manual. This unit may be close tou yours.
https://docs.google.com/file/d/0BzIi...it?usp=sharing