The reason the First Watt sounds like it does is its class A. Class A makes more heat; you're not going to find a cool running amp that is class A, so if you like the sound I would find a way to deal with the heat. Putting it in a refrigerator BTW will not work- the refrigerator has to get rid of the heat and will do so via its heatsink system.
One simple solution is to have a vent placed in the room above the amplifiers locations. The vents are then ducted to a fan that blows the air outside if needed. This system can be very effective and is cheap.
One simple solution is to have a vent placed in the room above the amplifiers locations. The vents are then ducted to a fan that blows the air outside if needed. This system can be very effective and is cheap.