The amount of heat an amp will put into the room can be judged based on its AC power requirement specs (or its AC current requirement specs, which can be converted to power numbers by multiplying by the assumed line voltage). Although that judgment will be less precise for class AB and especially class D amps than for class A amps, since those numbers will vary considerably as a function of the volume and dynamics of the music in the cases of class AB and class D. But for example in the case of the OP’s class AB amp we know that the power drawn will be somewhere between 420 and 730 watts, probably closer to 420 than to 730 most of the time.
This assumes, of course, that the specs are provided by the manufacturer and are reasonably accurate.
Temperature measurements (or estimates based on touching the amp) may not necessarily be meaningful because for a given amount of power consumption (and hence heat generation) the measured temperatures will vary depending on the design of the heat sinks (the more substantial they are and the more efficiently they radiate heat into the room the lower their temperature will be, everything else being equal), among other variables.
The amount of heat put into the room by a component is proportional to the power going into it minus the power going out of it. But since nearly all speakers convert just a small fraction of the power going into them into sound, with the rest of that power being converted into heat, the AC current or power drawn by the amp can be a useful indicator by itself.
Regards,
-- Al
