"Water vapor causes some deviations from the ideal behavior as at typical tire temperatures and pressures water doesn't quite respond as an ideal gas. Maybe the air you have in the tires isn't particularly dry."
Just a guess. You might want to try bleeding the existing air from the tires and filling them again with . . . . KNOWN DRY AIR! Having filled the tires with excess humidity may be an issue. 20 psi change from cold to hot is a lot especially in winter time. I'm generally not a fan of using nitrogen in RV tires but that would be another option if dry air doesn't help.
Edit: Do all the tire pressures rise equally? Have you checked the tire pressure with a KNOWN GOOD MECHANICAL GAUGE to confirm that your TPMS is reading correctly and that the known good gauge and the TPMS are reading consistently? In aviation you really need not one, not two, but three independent ways to confirm the accuracy of your data to be confident.
Chum lee