There is nowhere else for the heat to go.
Aren't you forgetting that the efficiency of a thermodynamic process is proportional the ratio of the differences in temperature and the ambient. If the Bitcoin mining chip is not as hot as the coils, then it will not be as efficient as the coils were. Also for example a hair dyer needs all the heat transfered within a short period of time, and if the heat transfer is slow not all of the heat may be extracted to the hair and instead wasted to the ambient. So somewhat less than free mining.
No. Work out the actual transfer equations if you like, but it ends up being an equivalence. Energy in = heat out. Or the device self destructs.
I am speaking about the efficiency of transfer on the time domain. Of course if there is no time involved, all heat reaches equilibrium. Thermal processes are uninteresting if there is no time domain.
How is it that my hair dyer dries my hair after i turn it off but my mining chip is still hot? You've got have a large heat sink in order to move the heat efficiently in time.
Device doesn't self-destruct if the duty cycle is not greater than what the heat transfer sink can deliver.
Heat sinks are often the most expensive part of the entire design. And there is a diminishing return. The heat of a mining chip is I believe very concentrated into a few mm
2 versus coils which cheaply spread out their heat over a large surface area of air flow.