I have looked at this issue a bit read a bunch, there is a crap pile of misinformation on the net.
Now I am not saying this is gospel, only my own understanding. The heat in an auto Trans comes from the slippage in in the torque conveter,and pressure pump.
There are many who believe the radiator cooler is to warm up the Trans oil. I believe this to be bogus info.
The oil leaves the torque converter at what I am betting is much higher temperature than normal running coolant Temps. Where it is cooled to 180-200°, then returns to the Trans to work the clutches and pistons, then drains into the pan.
Most oil temperatures are measured in the pan, so this is an average temperature.
Many opinions on to cool or not. I am undecided. We all know engine oil needs to be 180° to reduce wear. Now why would atf be different? I am unsure.
My stock 4l80e in my 01 ran just under coolant Temps, with factory cooler configuration. @195° by factory guages.
I add the derale cool pan, pictured above, the Trans Temps now run @155-165°, and takes some time to get there. All else is factory.
Just some thoughts, and I welcome any all thoughts theories or studies oil Trans oil cooling.