transmission cooler

I always used the local temps as to which way it goes, and this may make sense to you.
In hot climates I run the cooler before the radiator as it helps with the engine cooling a little also, and in cooler climates after the radiator because the engine doesn't need the help cooling.

The idea of not running it to the radiator at all is not because people are afraid they will get trans fluid in the coolant, it's because it would get coolant in the trans.
Antifreeze coolant and water both will disolve the adhesive holding the clutch materials on the discs and bands and pretty much instantly destroy the trans.
(Long before you noticed anything was wrong)