The whole cold pressure thing is interesting, it’s done to get a level of consistency and make it simple for Joe Public. Gas Laws state that the pressure for a fixed volume of gas is proportional to its temperature, as per Catman’s equation, which is great in theory and so cold temperatures are a perfectly reasonable way of setting the operating pressure of our tyres.
In practice, because there is a variable amount of moisture in the air in tyres and that moisture has a different relationship with temperature as well as affecting the rate at which the kinetic energy is converted into thermal energy (so tyre warm up) so it would be better to set the hot pressure, but this is a bit complicated for people who drive **** boxes.
A good example of this is my daily BMW, it monitors both pressure and temperature on its TPMS, and gives recommended pressures based on the temperature. To get any level of consistency (by consistency, I mean to get the hot temperature bang on because having it one PSI out messes with my COD) I have to set the pressures after a long drive with both the wheel and tyre up to temp. So the best way, if you are bothered by that sort of thing, is to set the temp cold, drive, check them hot, adjust them, drive it and see how it feels, find a good hot pressure and set it to that going forward. And yes, to do that you would have to be completely mad. Flibble.