Disc size is changed for heat dissipation.
The amount of pots in the piston has nothing to do with heat dissipation.
disk size is changed for dissipation and in some circumstances to act as a larger reservoir. (dissipating heat is about re-preparing for the next application, the reservoir requirement is about being able to absorb a large enough single application during which there is little time for dissipation)
Alloy 4 pot calipers dissipate heat better than standard single piston iron calipers do, as you say its not really down to the number of pistons, its down to the material and the rest of the design.