My dryer will not shut off in the automatic cycle...it will run forever. It will turn off in the timed dry setting. Is this something called the cycling thermostat?

I am assuming that you do have heat.

You may also want to check for an open or grounded element and the resistor (Item 80 in Section 1). This resistor drops the 240 volts down to 120 volts for the timer motor.

In auto modes the timer motor gets power through the heating coil when the heater is turned off. So an open or grounded heater can stop it from advancing.
Depends how it is wired and since this is a GE I do not have access to a wiring diagram. Perhaps yours is in the control console.
Below is a link that gives examples for a couple GE's so at least you have an idea how they are wired.
http://www.applianceaid.com/diagrams.html

Check the heating coil.
Unplug the unit and both wires to the coil.
Check it with a meter, should be around 20 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. This can cause it to run on high and the thermostats cannot regulate it so the thermal cut-off blows.