I don't know where the exposed transmission fad came into play in the rat rod world, but you might want to rethink that. I have a friend who has a 41 Chevy rat truck. It has a dual quad 383 with a 727. He decided to expose the transmission in his build with expanded metal. Only after a few minutes of driving, it gets hot as HELL in that truck. So much so, that he only drives it on cool evenings and in the spring and fall. He's going to put a solid floor in it probably this spring. It's one of those ideas that looks cool but doesn't WORK too well.
Although, if you use a manual transmission, I don't think the heat buildup will be nearly as much.