[freebeard]

...the idea is just crazy enough that it might work...

1. Your aluminum bellypan could be one thin sheet with a bead-rolled, branching channel soldered or epoxied to a thicker aluminum sheet. There would be hot spots on the upper, inner face and a more uniform temp facing the air stream.
   
2. I [unfortunately] don't have a reference, but in the 1950s someone built a Porsche racer that had the cooling duct end in a plenum about as big as a truck muffler that had the exhaust positioned inside as the only energy input into cooling. I don't know the result.