I've never had an issue running a trans cooler without using the rad, (stick rad, with auto added through the extra cooler only) in the northwest corner of IL, for 12 years in a snow plow. Same trans, not rebuilt. I fail to understand why you want to reheat the trans fluid up to 200+ degrees before you send it back to a hard working trans.

But, if you feel you need the rad cooler, have at it. To be useful, the rad cooler would need to be the last cooler the trans fluid passes through before returning to the trans.

Mount the cooler in front of the AC condenser, and point the hoses whichever way is easiest to connect. Gene