I think I know where itchy is coming from, especially if it is mounted horizontally, it will just gather everything on top of it.
Nakkas, where abouts underneath were you thinking? It could possibly be mounted out the back, in a vertical position, but it would cop a hiding I would expect.
I worry about my trans, especially when towing, even just my little 6x4 heats it up over 100*C.
I only have a alloy finned cooler at the mo, which is useless at slow speeds and has no way of forced cooling. I spose I could spray it with water but then you have yet another thing to check.
cheers