Before leaving Houston, I carefully set the pressures to 65 psi all-around, on a typical 85-degree July morning in Houston. While underway, the temps varied considerably, with the rears running 10 degrees hotter. The hottest was the right rear, which I figured must be because the exhaust runs close to that side. Pressures were all different and all over 70 running, with the rears approaching 75.
But then, on one 50 degree morning in Yellowstone, the low pressure alarm went off as soon as the sensors started to come up, as I was leaving the Fishing Bridge RV park. One of the rears was below the 55 psi low-limit I'd set.
Pressure is directly proportional to absolute temperature. PV=MRT Boyles Law
so 85oF = 545oR
50oF = 510oR
Multiply (65 psig ) X 510/545 = 60 psia
5000' altitude the air pressure is 2.5 psi lower
10000' altitude the air pressure is 4.6 psi lower
So your experience is what would be expected.
All tire manufactures say check pressure when tires are cool and leave alone.