The first thing to do with virtually any amp is to exercise the effects send and return jacks. Just plug and unplug into those jacks a bunch of times, or try playing with a patch cord in the effects loop. Same for other jacks like auxiliary inputs.
Try isolating it to the preamp or power amp by breaking into the signal chain at the effects loop.
Otherwise, a "thermal intermittent" can be tricky to diagnose, but all amps have familiar pain points, namely internal connectors between circuit boards, and the points where the jacks solder down to the circuit board.
Unfortunately, the little GK combo's are a chore to disassemble. I've got one. And I have to say this: Don't open it up unless you're qualified to work inside mains powered gear.
Oh, and make sure it isn't your input cable.