Even without temp (only pressure) a TPMS can detect an unusual temp increase. I'll manually check my tire pressures at the beginning of the day and then an hour later. On a rainy day my tag axle tire pressures had increased more than the normal 10% and all of the other tires had not. I pulled over and using my IR temp gun found my tag tires temps at 125 and all the rest under 100. At the back of the MH I could hear a small air leak which was coming from the tag axle air pressure regulator. Turns out it was putting 100+ psi into the tag's airbags which was overloading those tires. Not sure why, and by turning the adjusting knob back and forth I was able to get it back to the 45 psi I use and this was five years ago.
Over time you learn what's normal and what's not.