Nitrogen in tyres

[hollus]

This makes sense. Those are larger, more complex molecules compared to N2 and O2, with more internal degrees of freedom to accumulate energy as vibrations. Hence they have a larger heat capacity than air (per volume, which is the relevant unit, per mass they are smaller).
They can absorb a larger amount of thermal energy with the same change in temperature, hence the tire will keep an equally constant temperature change while being subjected to larger differences in generated heat, or a smaller temperature change for the same difference in generated heat (between different sections of the lap). So the rubber temperature is kept more constant.
Gases like that R404A about as a large molecules as it is practical to use as gases...

I wonder which factor is more important to increase the rate of heat transfer to the different surfaces in the tire: the larger heat capacity compared to air, or the larger mass compared to air? But both go hand in hand, I guess.

[Richard]

The critical factor is the moisture content of the gas used

That was the point...Nitrogen doesn't hold as much moisture

Nitrogen can hold plenty of moisture, just like normal air. The difference is that nitrogen supplied in a gas canister is guaranteed to be dry due to the manufacturing process. Dry gas is much less variable with changing temperature than humid gas.

I'd have thought the oxygenation argument wasn't relevant to F1 due to the short life span of the tyres? I can see how it might be relevant to road cars with tyres last over a year.