With my 15 Ram 3500 only carrying 2,400#, I've seen my pressure go from 80psi to mid 90s. Back when I had my 04 Ram 3500 SRW hauling a 35' FW with a 1,600# pin weight, I left in the cool 65* morning with my tires at 80psi. After 5 hours of towing and the temps climbing to almost 100*, my PSI climbed to about 106psi with the tires measuring 115*.
Just remember, never lower the PSI due to the increase from traveling. The PSI is to be checked when the tires are cold which means with less than 1 mile and before the sun shines on them.