... What does this do to the sheathing??! By allowing the sheathing to 'accept' the heat, and allowing it to penetrate to the underside of the sheathing where it's 'reflected back through the sheathing' would just break down the wood fibers in the sheathing. This principal may work well with metal shingles and such but with wood, I think the aging process of the sheathing would be tremendously accelerated. As bc says, you'd need something like that works like the space shuttle 'shingles/sheathing' to do what you describe. This is why a 'couple' of us are a bit perplexed that you'd put a 'reflective barrier' on the UNDERSIDE of the sheathing as opposed to the top-side. (This was the original question from the Poster.)
FWIW, I certainly wouldn't buy into ANY concept where you put the reflective barrier on the underside of a roof. (Unless, that is, the shingles themselves had a radiant barrier on their underside, and they can 'handle the heat buildup' as you describe.) Your description is why some roofing material is made from metal. Simply put, it will get hotter than the surrounding temp. and radiate upwards and outwards.