Heat gain/retention in asphalt shingles under Stone coated steel, radiant barrier?

Whereas many painted metal products have special heat reflective pigments in the coatings, that typically is not the case with most stone-coated products. Therefore, the actual reflectivity of most stone-coated products comes from color usually -- light colors being more reflective. However, the energy efficiency of stone-coated products comes a great deal from the integral airspace that separates the metal from the roof deck, blocking conductive heat transfer. Adding a radiant barrier on top of the roof deck or even in the attic can indeed be helpful and is sometimes done with stone-coated products. I do not have any empirical test data though. TEK is not a member of the Metal Roofing Alliance but they may have data of their own. Making sure the attic has proper ventilation is also usually very helpful.