OK. If your drive is not within specs, your MosFet may not turn ON and this means it will be a resistor instead of a closed switch with low resistance.

Now, choosing a MosFet with 20Amps does not necessarily means that it will stay cool. For this to happen you must select one with low Rds ON resistance. Many recent ones do exhibit also that low Rds.

Finally you want it to be SMD or TO-220 ?

Ioannis