I hadn't thought about that, but looking at pictures of cupolas, that makes sense. Such would play a similar role in thermal regulation as a whole-house attic fan in extracting hot air from the house. I find myself wondering now if a cupola could supplant an attic fan, or if not, complement one enough to reduce the size/power needed.

It seems to me that done right, a cupola would also make a great source of indirect natural light.