Paul I could be wrong but I believe that stainless steel does not disapate heat faster than steel. But you seem to be more directly concerned of the sun's radiant heat soak into the barrel material, I think those temps pale to temps achieved by firing a good few slugs. Anyone?

Maybe it stays hot for what seems a long time after firing because, hey, it's a big chunk of steel. I would guess that off the top of my head the barrel wall thickness of my Ultra 12 is three times thicker than a typical 12 barrel.

Note to self: Put calipers on barrel walls also.