Larry - I’m too far away from thermodynamics classes to feel confident, but here is a stab at answering your questions…
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There are 4 types of heat transfer in this world (that I’m aware of anyway!) - conduction, convection, radiation, and phase change
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When it comes to tires, I think everyone can agree that the primary source of getting a tire up to temperature while on-track is from the conduction at the high friction interface of tire/track (contact patch) as opposed to radiation (thanks sun), convection (tire is not a fluid or gas), or phase change (one would hope!)
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As friction heats up the tire via contact patch friction, the tire heats up both the air inside the tire as well as the rim via conduction. We’ll leave out the convection going on inside the tire for simplicity.
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Heat transfer occurs at a lower rate in materials of low thermal conductivity than in materials of high thermal conductivity. In the case of wheels, aluminum is higher than magnesium - so as the tire generates heat, an aluminum wheel will get hotter faster than a mag wheel
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My head already hurts, but I’ll try this anyway - when an object is heated, it’s heat capacity determines how well it stores that heat. Aluminum has 2 things going for it vs. magnesium on this front - it has a higher heat capacity, and aluminum wheels weigh more and is a bigger “thermal mass”
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So if we’re on a cold or wet track, the tire builds up heat very slowly because friction is a lot lower at contact patch. Thus, the air in the tire heats up slower and the wheel heats up slower. Aluminum helps, as it will both warm up faster and hold on to the heat better in these crappy conditions than magesium would. The “cool” part (hahaha - thermo dad joke) about this for us karters is that that aluminum wheel will also release its heat back into the tire better than magnesium… so in parts of the track where the tire isn’t generating much heat through friction (long straight), the aluminum wheel helps keep the tire itself hotter than a magnesium wheel would.
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The inverse of this is why magnesium wheels are better on a hot day/track - they don’t build up or store heat well, so they stay cooler than an aluminum wheel. They don’t contribute to warming up the air inside the tire like an aluminum wheel does, enabling a higher starting pressure, which itself helps heat up the rubber faster.
There’s more to it all, but that’s the bulk of it. I think. Maybe.