Yep. The other thought is to use the existing radiator and just mount it outside in the shade. I might need a larger pump to move the water longer distances, maybe.
Another thought would be to stick an AC unit in the water with it, then pull the heat off that way. Or something even weirder.
C
AC units can be expensive. I could see an old window shaker AC unit or a dehumidifier off craigslist working really good for this though.