I live in North Texas and today is the 31st day in a row over 100! Supposed to hit at least 108 later this week. Needless to say, I'm limiting my riding to before 10:00 am.
I put 42 in my tires "cold", but with the nightly temp only getting down to about 84, that's not exactly the correct way to describe it. My onboard sensors read about 2-3 psi lower than my gauges (quality digital).
This is a good example of what BDF was explaining. Since you are filling the tires at about 20F above the "cold standard", you would need to put approximately 44psi in the tires to have the same amount of air in the tire as 42psi at 65F (or 68F - I've seen both used as the stated "cold" temp).
Air expands as it is heated. More expansion = more psi. More air mass (volume? I regularly misuse the words) = more psi. The TPS in essence calculates the air mass by comparing psi & temp, and reports it as a compensated psi figure. If the air in the tires was perfectly dry and the display resolved 10ths of a psi, the display would be pretty constant. As with any electromechanical device, it is possible to have an inaccurate unit, but the tech is pretty accurate for the most part. The more moisture in the air in the tires, the more the pressure rise curve is affected as the tires warm up. IE, if your TPS moves a lot between hot and cold, you probably have a lot of moisture in your tires.
It may not be rocket science, but it is science & physics. A lot of riders seem to struggle with the concept. Since I have confirmed that my TPS matches my gauges at 65F, I set the pressure cold to target a 42 readout on the TPS.