Up here I have run the outlet straight to the inlet for months atta time,and several years in a row.The tranny is still working fine. At the extremes of temp like winter, it might not like that. Or on hot summer days. But this was behind a 73 stock teener with a 2800TC, and just bolt-ons/no cam.
IMO a stand-alone may be fine. If you put the cooler in the airstream a fan shouldn't be required. The tranny is only working when the car is moving. In neutral/and more so in Park; it will take a really long time to bring the oil-temp up.I think that is part of the reason the cooler is in the rad;to help bring the heat UP in the morning.
If you are worried about heat, you can always put a gauge on it.