Jay Smith writes:

Loose connector on the back of the GEM.
A friend of mines Bonanza had the same problem.
He would be flying along, and the GEM would go dead.

I've had that too. Reaching behind the GEM verified it. (Zip ties
are sure handy to have on long trips.)

The symptoms in this situation were different for me than what the OP
described. The GEM would usually go dead then, if it returned, would
take a moment to boot before doing anything useful. The "dancing
temperatures" is not consistent with that.

--kyler