If you primarily tow in hot weather I would install the extra cooler in the return line to the tranny. Actually a large trans cooler doing the whole job is better. Just disconnect the in radiator cooler. This will take a major load off the radiator by directing the heat from the tranny to the air/oil cooler and not the water.

HEAT is the number one killer of the tranny. It casues the oil to break down much quicker and also casues the seals in the clutch packs and servo's to harden and lose their ability to seal properly.

Unless you live in the arctic you wont have to worry about the tranny being too cold.

Install a gauge to monitor the temp. The best place to monitor this is either in the pan or better yet in the return line to the tranny.

180F is a nice place to be. 225F on a hard pull is OK anything over 250F is what I call the "Crispy Zone" and will rapidly shorten the life of the oil and the tranny.

A remote filter in the return line is also a nice addition. There are ready made units that have a bypass (Must have) These look just like a regular oil filter for the engine.
These will take out a lot of crud that an auto tranny churns out in normal opperation.
Change the filter when you do a regular service, then top off the fluid.

best

Robyn