Best way to think about tire pressure and temp?

[SCengineering]

I know the relationship between temperature and pressure goes as PV=nRT, but then how is this related back to contact patch size and heat of friction generated at the contact patch? I guess I am just a little bit confused on how to think about it since lower tire pressure (from a lower number of moles of gas in the tire before operation) increases the area of the contact patch which increases the chance that a given particle of air inside the tire would hit the (relatively) heated contact patch and "take" some of the contact patch's kinetic energy. In other words, it makes sense that lower tire pressure could increase a tire's average operating temperature since it increases the contact patch area.

As a counterpoint to the above idea, it also makes sense that just putting a greater number of moles of air in the tire before operation (which would decrease contact patch area by making the tire rounder), might also be able to increase temperature, since, even though there is less of a chance for an individual air particle to come in contact with the heated part of the tire, there are more particles.

Is it the case that increasing the number of moles of gas is more effective at hitting the heated contact patch more often (in other words, is increasing the tire pressure before operation better at increasing operating temperature?), or is increasing the contact patch area through a lower initial pressure more effective? I'd assume having more particles in the tire trumps increased contact patch surface area at generating tire heat, but I'm just not sure how to think about it. I guess it's also possible that the answer might depend on the temperatures and pressures in question. Any ideas/help? As a disclaimer, I'm sure this is a relatively rudimentary question, I just don't know that much about tires/gas chemistry.

[Jersey Tom]

Actually, none of those are really any of the mechanisms for how tires generate heat.. though changing pressure definitely will change temperatures, both globally and locally (spread).

Think about the mechanical properties of elastomers.. loss modulus.. and how strains are going to change for a given load as you change inflation..

[SCengineering]

Ah. I guess the assumption I was making while thinking about it is that the initial tire pressure, and thus the size of the initial contact patch (which, I also assumed would be sort of close to the average contact patch size throughout a tire's stretches and compressions), are really the only things that it is possible to control, for a given tire, before operation. I mean, I know it is probably relatively less important to worry about getting the pressure exactly correct for generating heat, and far more important to just get the correct tire size, spring rate, compound, matching of tires across front and rear, etc. before entering the track. I guess I just don't really understand how the temperature changing properties of pressure would be made important in the case of a tire where there are so many other variables to consider. Also, do you mean to say that tire temperature is generated more by compression/decompression (in a kind of internal tire friction, say, for lack of a better vocabulary), rather than the equilibrium temperatures and pressures of the gasses around it?