I've linked to a youtube video on disassembly for GE dryers of this era. That might help, should the problem be one which requires taking things apart.

This dryer uses electronic sensing to determine how much heat and how long to dry the clothes.

First thing to look for is whether one of the two circuit breakers for this dryer has tripped? They're supposed to be 'ganged' together so they both trip at the same time, but it doesn't always work that way.

Second, is a knob set to a wrong setting or a position in between settings?

Third, is there a blockage through lint or a foreign object anywhere in the air path? The vent has super sharp edges, so be careful when checking. It's not uncommon for a dust bunny to take up house right under the lint filter on these, just inside and below the frame for the removable lint filter (it may be fixed on your model but the filter frame can be snapped out in that case).

Fourth, with the heat set to the highest setting and the dryer on the 'most dry' setting, run it for one minute. Is the drum then really warm? Just barely?

Fifth, it's possible something you dried has built up a film on the moisture sensor/s. Especially cheap fabric softener dryer sheets and some of the 'eco' sheets can build up a film. When the drum is absolutely cool, try cleaning everything inside with some rubbing alcohol. 

If none of these help, it's time to cautiously look inside (plug pulled!)

A loose or intermittent ground contact or sensor contact to the drum would cause this symptom. So would build-up or another loose connection. A slipping belt?

Those are general ideas, but they should give you a direction. Somebody here who is more familiar with the circuits on these can give you more specific guidance, but they'll probably need the answers to the suggestions I've made, too.

Good dryers, I'm sure it's nothing you can't fix.

And very likely. I encountered a problem with an early '80s Miele in Germany which is similar in presentation. In that case, it was a loose contact to a drum sensor. When things cooled down and shrank, it made enough contact to restart...which took about 10 minutes.

Another possibility is that crazy belt sensor GE uses.