Stupid class A question

Most likely yes. Class A amps produce heat regardless if a signal is passing through and in many cases the current (and heat) at idle is greater than the full volume current going to the speakers.

@gs5556 Thank you so much!

Yep.  

You have a true class A amp.  Any amp that claims to be class and and doesn't make a lot of heat is not class A.

A friend of mine had a Krell KSA-250 class A amp. It ran about as hot as any class A amp I have seen. After about 10 years it needed major repair from so many internal parts having severe heat damage. Althogh a lot of people would think that's a pretty long life for a class A amp.l

The krell ksa 250 is not class A to full power, only up to about 28 watts or so.

Probably more. The only time Class A does notgenerate heat is when the power goes to the speakers instead. 

(Or maybe a water cooled dummy load.)

@Invalid,

Regarding the Krell KSA 250. True, it was only class A up to 28 watts, but it still ran very hot even at idle.

28 watts of heat.

More like what it draws in heat. Probably 250-watt light bulb or so. Most of the heat in class A is wasted but worth it to me.