When we went through the Big Horn mountains we had a stock 2008 GMC 1500 crew cab 4x4 with 5.3 and 3.73 rearend pulling a Jayco 26BH. It did the job but wasn't very happy about it at times. We were often around 15-25 mph going up with transmission temps as high as 240F with the reduced air flow over the cooler. I left my transmission temp on the DIC displayed all through the trip. Before going on that trip I spoke with my local GMC dealership and was told 240-250F was ok for moderate periods of time. He had told me that transmission overtemp/warning was at 270F. We upgraded to a HD after that but if I had kept that truck I would've put LT tires on it and an electric fan to push air across transmission cooler in low speed pulling.
Just make sure everything is in order and maintained. Don't be afraid to let your truck pull some RPMs and do downshift on the down grade to save on brakes.