As first thing try replacing the thermal fuse.
The thermal fuse is located in the blower housing, near to the exhaust at the back of the dryer. The thermal fuse cost is only few dollars. Before replacement it can be tested reading Ohms with a multimeter. If the multimeter set on impedance reads infinite Ohms (No continuity, same as on air), then the fuse must be replaced. A good fuse must read low or zero impedance.
If the thermal fuse is OK, the next parts to test are the thermostats. On GE gas dryers there are at least two thermostats. One is a control of themperature, the other is an high limit. High limit is hosted on the blower housing, near to the thermal fuse. There is one or two thermostats near to the blower wheel. Often there is a safety thermostat near to the burner. To get details on the specific model check the schematics tucked inside the appliance or available online.
The thermostats are tested reading Ohms at room temperature. If any of them returns no continuity at room, then the thermostat is faulty and must be replaced.
If the thermostats and fuse are OK, then the next step is checking valve and igniter. The igniter or glowbar is tested energizing it and observing if there is spark. The valve is tested reading Ohms on solenoid with multimeter set at Rx1. If the solenoid has no continuity, then the valve is faulty. There is also a flame sensor that can be tested reading impedance or jumping its contacts.
If all the parts listed above are OK, then wiring and electronic timer control board must be tested reading voltages at contacts.
The problem is likely the thermal fuse or one of the thermostats.
Apart replacing the part, ensure that the hoses are not blocked , and that there is no lint inside the machine. This may have caused the fuse blowing.Here a general diagram that can help you in identifying parts.
All tests must be done by a trained technician.
To get a technician on site , or to get a quote on repair ring the number listed on the owners manual.You can also get an US technician contact using our directory:Contacts.
To get parts ring GE at the number on manual.
You can also use one of the websites listed here to get parts and diagrams:Where do I find parts and diagrams for my Appliance?