Look at the red regions of the attached Fig6 and Fig8 from the IRF510 data sheet. If you operate it with Vgs ~10V, that shows what the Vds will be for whatever current (Id) your load draws. The power dissipation (heatsinking requirement) for the FET is the product of Vds and Id.
The IRF510 is an old, not very good NFET.
You never answered the comment about using a NFET if you have a Low-side, grounded load???? If you use an IRF510 in a circuit where the drain is connected to 12V, and you put the load between source and ground, the gate will have to be driven to +22V to saturate the FET.
Are you prepared to do that? It usually means using a charge-pump, or another power supply to get the higher gate voltage.