When switching on or off, there are short periods where the channel resistance is low, but not fully to RDSon. The main factor is when conducting currents, P=I^2R, with R being RDSon, and I being the current through the MOSFET.
I agree with Gerty. MOSFETs are best used when they are ON or OFF. No heat to dissipate in the off condition. Only the little ON resistance X current squared gives you the heat dissipated when completely on.
The real heat is generated when partially on, (Linear region). The voltage difference measured across the MOSFET D and S AND current flow through the MOSFET means power is put into the MOSFET. It has to dissipate that power somehow (heat, light or work). The MOSFET doesn't do work or generate light so it will only get hot.
Twinkle twinkle little star,
Power's equal I squared R.
That is a somewhat flippant way of saying:
Heat is proportional to power.
Power is dissipated when a current flows through a resistance.
Changing the resistance of the channel for the same current causes a linear increase in power.
Changing the current in the channel for the same resistance causes a quadratic increase in power.
Back when I was designing switching power supplies we almost ignored the "on" state power. The major power loss in a switched device are the turn on (small) and turn off (huge) losses.
Of course, if you're running in a linear mode there are no switching losses, but lots of power being burned off.