Class A is always going to run warm.
Companies like KRELL and Westminster Labs say their amps are Class A and they run cool. The KRELL Duo 175XD that I owned ran cool and sounded like other Class A amps (maybe better). That was up to 175 watts of Class A, when needed. I also own a great Class A amp, the CODA #16 so I have a good frame of reference for the KRELL.
Companies like Gryphon say that the iBias based Class A such as the KRELL are not real Class A. You need to waste electricity for true Class A.
The new KRELL KSA i400 is the next version of what I owned. I expect that to also run cool-ish. That amp is 400 watts Class A at 8 and doubles to 800 and again to 1600. I think it is only 400 watts class A at all impedances.