I did an amplifier like your talking about. It sat behind the seat of my GMC 4x4 pickup, so I HAD to have cooling.
I mounted a fan to it, and powered it from the power switch. HOLY MOLY, that was a mistake! It was LOUDER than the AC Blower on HIGH!!!
That's when I discovered lifting the fan about half an inch to an inch above. Once I did that, A LOT of the noise went buhbye!
SO, I had to make it better. I put a half speed switch on it (electronic) that worked like this:
Power on to the amplifier, it would run the fan at half speed.
As SOON as it keyed the relay, it would bypass the resistor (or pot, in your case), and fun full speed.... I put a steering diode in the positive lead to keep the fan lead from keying the linear, and a transistor switch to short the resistor.
Shortly after that, I took the 'key' circuit out, and put in negative keying..... ground to an RCA jack keyed the amp and supplied bias.... AS WELL AS working the fan speed switch.
You COULD do the same thing with the thermostat switch you want to use... Just wire it in like normal, and put the pot ACROSS it... Then, it will short the pot out and run to full speed when the amplifier heats up.
I'd say that's a lot more work, though, for a solid state amp. If you're HELL BENT on a thermistor, I'd have the thermistor in my keying line, but backwards: IE, it would be SHORTED when the amp was cool, and open when it got hot... THEN, you can't key the amp if it's too hot
--Toll_Free