The trans cooler will need air too. Some of those "fins on a pipe" won't cut it when your crawling at 2 mph.
Your donor should have a trans cooler in with the rad ... use it.
Also ... Istall a drain plug in the tranny pan. You'll have the pan off (or should) to put in a new filter. Changing fluid/filter without a drain is not fun. I dropped the pan, and didn't do a plug. I know I'l regret it next time.