I found the same issue with our Carlisle tires. I changed tires and added the TPMS at the same time. Never knew the temps and pressure went up like that while driving.
After checking with the dealer as well as a relative in the tire business, the answer was "this is normal". Both recommended keeping an eye on the pressure and temps primarily looking for any inconsistencies among the tires being monitored. They assured me that the tire manufacturers allow for the increase in pressure and heat in their engineering. I can even notice which side the sun is shining on by several degrees
I once noticed one trailer tire about 15 degrees hotter than the others. Turned out the brake on that wheel had seized slightly creating the added heat. Having the TPMS saved our vacation that summer!