Surprises me that your truck doesn't have one on it? I have a 2009 2500HD with tow package, 6.0 gasser. Mine has a factory cooler on it. I was pulling a 29' Wildwood. My tranny would run around 175 to 190 with minimal hills. Sometimes it would hit 200 on occasion. I would definitely recommend getting one if your truck doesn't have one. One of hardest things on the tranny is extended periods of high heat.
Quick question, what kind of mileage do you get. I usually get 7 to 9, occasionally 10 if I'm lucky (tail wind). My truck has 3:73 rear gears running the 6 speed auto. Wish I ordered the 4:11 now.