And you have already calculated that the MOSFET will actually heat up? Since the current would anyway flow through the MOSFET, whether switched or not, the channel on-resistance will make no difference. So the only effect heating the FET would be switching losses. For a DC motor (the fan motor is DC?) the switching frequency can be quite low, resulting in negligible switching losses. Honestly. For argument's sake say you have a 100V 10A motor (~1 kW) and you hard-switch the MOSFET. Say your FET switches in a leisurely 500 ns. The worst case instantaneous dissipation during the hard part of the switching sequence would be 1 kW. Simplistically calculating that over the 500 ns duration that would mean 500 nJ of dissipated energy. Say your pwm frequency is 500 Hz so you dissipate that 500 times a second for a total of 250 mW. This while switching a 1 kW load. For 100 W load the dissipation would be ~25 mW and so on. If you manage to switch briskly so that the state changes in ~100ns which is maybe a more typical value for a well tuned circuit, your dissipations fall to 50/5 mW, the latter being truly insignificant already.

But of course, if you made promises then there is no helping it ...