Hmmm... although it's not 100% clear what your thermostat is, I would guess it is a device with a relay built in to turn on the fan? If so, then it could be one of two things. The fan is probably an inductive load (motor) and as you switch it, you will get a large current spike. If this is plugged into the same mains feed as your amp, then you may hear this as a pop. You could filter this with a mains filter, and seperate the feeds to your amp and the fan by using different mains feeds. It could also be radiated RFI from the relay as it switches the load - a current spike could result in flash-over between the contacts at the time of the switch. If your amp is not properly shielded, this could cause the pop. You would need to solder on supression caps to the relay of an appropriate voltage rating to stop the spark. Mind you though if your amp was that sensitive and poorly shielded, I would buy another one . I have no idea how big your fan is, or how much current it takes - but if it takes enough current to cause flashover and RFI then it is either too big, or faulty, or the relay unit is duff/using poor relays/etc. I suspect this is a case of "You pays yer money...."

A mains filter and seperate feeds would be the first, easiest solution. A second step would be to use a more expensive switch that uses a thyristor switch instead of relays; after that, I would start drilling big holes in the back of your cabinet....