When I was towing a 12k FW with my diesel, I've seen it go from 80psi @ 70* in the morning to almost 110psi after 300 miles and temps rising to 95*.
Just remember, don't let air out just because it goes over max pressure after driving. Tires are to be checked when cold which means less than 1 mile of driving and no sun shining on them. The tire manufacturers design in the rise of pressure.