Your friend must pull his hair out at your inability to accept a simple, experienced answer. He is right, but you seem determined to prove your thought process, even though it has little operational applicability. A simple question resolves the problem, "Does this amplifier run hot?" Beyond that all the hypotheticals are meaningless.
It reminds me of the story of two men who are in a hot air ballon and become lost. They see a small town, lower their altitude and ask someone on the ground, "Where are we?" The helpful citizen yells back, "You are in a hot air ballon!" Technically correct, and completely useless information. If I may be so bold, you are seeking technical information witch is fairly useless to success in building the audio system (i.e. cool running) you desire. :(
Class A and tube amps typically run warm to hot, but there are exceptions
Class A/B you can find hot ones, medium and cool running ones
Class D never runs hot; at least I have never encountered one which runs hot
Of course, all this has little to do with sound quality, which ranges up and down among all classes of amps. I suggest that seeking an amp which operates with the least percentage of heat loss is a grand way to build a mediocre sounding audio system.
A discussion of maximizing one's speaker efficiency also has nearly zero relation to the question of how hot a room becomes with use of a certain class or model of amp. :(
You are way overthinking the issue, and it seems you struggle to accept simple, straightforward advice from experienced persons. I wish you success.
