Empeg in front of a vent blasting cold air will fix it for half an hour or so, so it looks like the audio circuitry is overheating and cutting out - btw, my digital temp sensor doesn't work, so one of the audio components must be hitting an internal temp cut.

It is more likely that the heat caused a drive to fail rather than any audio circuitry. The disk drives are more suceptible to extreme temperatures than the audio electronics. Also, heat can sometimes make a spotty connection (such as a bad crimp on a disk drive cable) fail.