I have a 2005 Silverado 3500 and the stock cooler is marginal for towing in the mountains in the summer. I first installed Mag Hytec pan and synthetic fluid it helped but when pulling on route 89 south of Stowe, VT on a 95 degree day with very high humidity, the transmission temp got over 200 degrees for a short time. I did some research and many people driving with a 4L80E are using a Tru-Cool 40K as a replacement for the stock cooler. When towing now the transmission temp runs about 160 degrees. As far as overcooling, the fluid is preheated in the radiator and the Tru-Cool has a provision for thick cold fluid or you can add a thermostat. It is my understanding that the thermostat actually makes the transmission run warm.
My reason for upgrading is that we are now retired and going to visit many national parks and they are in or around the mountains.
Good luck.