I have a 2012 Ram 2500 with 5.7 Hemi, 4.10 rear pulling about the same weight. Transmission temps runs about 170 degrees towing and not towing. I had a 2007 Ram 1500 5.7 Hemi, 3.92 rear pulling same trailer and it would run about 180 degrees when towing.
2012 Ram 2500 Big Horn Crew Cab 8' box
5.7 Hemi, 4x4, 4.10
2015 Jayco Eagle 284BHBE