Back in my motorcycle days tire pressure for a particular load was always a hot topic of discussion. Owners' manuals typically give different tire pressures for various loads (eg, one up, two up, luggage loaded). One of the much touted ways to select the correct pressure for the load is the "4psi rule."
Pressure increases with heat (about 1 psi for every 10 degrees of temperature increase to the best of my recollection, whether the result of the weather or rolling friction). As the tire rolls down the highway, it produces heat and temperature always increases, which increases pressure, and is quite normal. However, too much of an increase in temperature and pressure is undesirable, and may indicate initial under inflation. Correct inflation can be determined by measuring the amount of pressure increase and adjusting accordingly. Those who claim to know such things state the so-called rule here:
https://www.tyrereview.com.au/tyre-advice/the-4PSI-Rule
Keep in mind, of course, that the tire can only take so much. Increasing pressure to compensate for excessive heat and pressure rise becomes dangerous if the tire is then exceeding its limits. There is a load/pressure limit for every tire. If not called upon to carry its maximum load in a particular application, the vehicle inflation recommendations will be less than the maximum inflation specified by the tire's manufacturer.
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