There is no difference between the materials of solder masks. The color is just an additive, sort of like the food coloring additives.
There will be a miniscule of difference between white and black PCB, for black body radiation. It is really small unless the temperature of the board is very high. Ignore it.
Solder mas is not a heat spreader, it conducts heat very badly.
Via stiching does help, but only in the first mm or so away from the component.
Copper pour helps a lot.