I would bet if you ran a pan with powder coating and with out coating you would find the raw pan cooled better. My friend used to run a street rod shop and one of the companies they were a vendor for sold bad ass Aluminum universal cooling canisters for power steering, radiator fluid, whatever. They were finned long round cylindric tube style cans. They sold a raw finish and polished finish version. They said the polished version did not cool quite as well as the raw finished one did. Not a huge amount, I'm talking a few degrees.
Think surface area and poors. You smooth it all out and you lesson the peeks and vallys and polish out the poors of the material. So your effectively lessoning the surface area of the material, all be it by a very small amount. Powder coating I doubt has thermal barier protection properties in it at all that would affect cooling or heating. But, covering the raw aluminum thats a known heat sink type material would probably not allow the aluminum to draw heat in as well, effectively lessoning the cooling capibility of the pan itself. Not to mention your smoothing out the surface area.
Its the same princible as inside an intake chamber. It used to be thought that a highly polished intake was delivering fuel and air faster, that may be true but you lose the atomization of the fuel, or the turbulance created by the rough surface of the walls of the unpolished intake. A sanded flowed head with swirl polishing works awesome but it is NOT polished smooth. In a cylinder in a motor, Swirl marks catch the oil for lubrication, or oil retention. When those marks are gone from wear oil just runs off and you lose oil retention. The peeks and vallys are like swirl marks in a way, that catch the air for cooling, smooth it out and you lose cooling effeciency.
You want the pan to get hot so the air passing over it cools it down. If you cover it so it does not cool as well your raising internal temp of the tranny or motor. Make sence? The very best kind of coating you can have is one with properties that draw heat more effectively then aluminum does. That would draw more heat into the pan for cooling. There are such coatings but there expensive and not worth doing. There are also coatings that have thermal properties that resist heat. I coated the top of the piston in my dirt bike with a thermal coating designed to resist heat, to protect the piston. It kept the heat in the combustion chamber where it needs to be for a quality and complete burn of the fuel for power. Damn, for a dumbass, I sure sound smart, like a scientist.
