As an example I have had my truck tires start in cool temps in PDX OR cold tire at 80 psi. Near end of day.
In Redding CA air temps were 115F truck tires were 94/96 rears tire psi. That was heavy towing. As said "Cold inflation" and all tires heat up with use and PSI increases. If you set the TPMS up to see tire temps, likely none will be exactly the same. That's normal also. Tires facing sun will be higher than ones not. Side to side might be within a few lbs psi.
2013 24RKSWE (27ft TT) Cougar 1/2 ton series
2013 Ford F350 4x4 CC 6.7 engine, 8 ft bed 3.55 rear end lariat package
Retired from Oregon State Police in 2011 than worked another 9.5 years as a small town traffic cop:
As of 05-2020, I am all done with 39 years total police work. No more uniforms for me.