alt Hacker NewsWe only know that the large and the small motor deliver the same power. I don't see how we can conclude from that the temperature differential is also equal. In fact I would expect a smaller motor to have a larger temperature differential, because the heat is produced concentrated in a smaller volume.
Yep, you're getting it. Same power, same efficiency, same power dissipation, smaller motor, smaller dissipative area, higher temperature.
The other assumption I probably should have stated is that the two motors are made of similar materials with similar temperature limits. We know the ambient temperature and we know the maximum temperature of the materials used. So for a component made of those materials, existing in that ambient temperature, with an additional heat load proportional to the waste heat in the motor...
The ability to shed heat (assuming similar forced fan cooling, as we were) determines the amount of power we can deliver to the device without increasing its temperature.