While sniper is correct regarding temps and transmission fluid, given your location (Florida), I don't see an issue.

I had a factory trans cooler off a cop car that was as big as an AC condenser, took up the entire space in front of the radiator. From the factory, the fluid went thru the radiator first, then the cooler. When the trans cooler in the radiator failed, I ran just the auxiliary cooler. I ran the transmission this way for over 100K miles without issue.