While a darker roof will heat up faster, it will also bring in more heat. The ASV will be quite effective. I see no reason to choose a light colored roof if you do not want that but ultimately a light colored roof will have greater reflectivity and be more energy efficient.
I am planning on having a stone coated steel roof placed over my asphalt roof.
I am going to have them place a radiant barrier under the cross-battens.
I understand that the cross battens allow for above sheathing ventilation (ASV) and as the metal roof heats up, this creates convection current resulting in a thermosiphon. The hotter the metal roof panels get, the faster the convective air flow, and the more heat that is removed before it can enter the attic.
The question I have is, in this situation, will a darker colored metal roof panel heat up more and create a more effective thermosiphon, than a lighter colored metal roof panel?