Assuming you've checked the supply & control wiring at the amp while the fault condition exists it's probably a faulty component or marginal solder joint within the amp itself that responds to temperature. It could be a defect in the amp's PCB but that's less likely in my experience.

If it were my amp, I would rig it up on a bench with a power supply and attack it with a hot air blower and a can of freezer spray. This way you should be able to carefully apply heat/cold to various sections of the circuitry and observe the fault come and go at the same time and you can narrow down where on the amp's circuit the problem lies. Once you know where the fault lies you can then inspect/resolder joints in that location, if it's a faulty component you'd need to identify it and locate a replacement. It can sometimes be a little hit and miss adopting this approach and sometimes there's no substitute for proper fault finding using conventional electronic test equipment.
If you decide to give this a go you could use a conventional hairdryer on slow speed with a home made funnel attached - you need to be as accurate as you can be with this. Freezer spray is available from electronic hobby stores but at a push you could use a can of air duster upside down!
Of course, this is all assuming you have a fine tip soldering iron and feel confident using it in your amp - it sounds like it might be a nice one and in which case you might be better off having it repaired professionally.