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.
2015 Ram 3500 4x4 Crew Cab SRW 6.4 Hemi LB 3.73 (12.4 hand calc avg mpg after 92,000 miles with camper)
2004 Lance 815 (prev: 2004 FW 35'; 1994 TT 30'; Tents)
I still have add-on TPMS I bought like 15 years ago for my motorhome at the time.
If you have metal tire stems - it works very well. In case you have leek, you will get warned.
Leaving the monitor on overnight will give you theft warning as well.
Since then the market was flooded (I paid small fortune to only manufacturer 15 years ago) so I would go with what local guys recommend.
Getting it local solves potential warranty claims faster.
Mine are set at 80 cold; usually they run in the low 90's, and I've had them hit 99 on the highway in the summer. I wondered if the TPMS was maxed out at that point. F350 SRW, loaded to roughly 7200 lbs on rear axle.
I had the factory TPM disabled on my truck.
The light would come on a 65 psi.
Empty I run 50 psi in the front and 45 psi in the rear.
The tires wear even running those pressures.