Nitrogen has been proven to be less affected by temperature changes than just regular old compressed air. Racing teams have been using it for years. Now auto dealers are filling customer tires with it, too.
As an aside, when I helped a buddy in the pits with his open-wheeled sprint car (ran on asphalt, not dirt), we'd adjust the tire pressures right before the race. We'd also take pressure and surface temp readings as soon as he came back into the pits. There were always psi variances. We knew that the tires like a certain amount of pressure for optimum grip, so we started out with them a bit lower (been to long to recall actual numbers) than ideal, and as the car went round and round, they warmed up and went into that ideal range.
We could also tell if there were variations between races by checking end pressures/temps.
We eventually went to pressure-relieving valves that could be set at the maximum pressure you wanted to run, and would bleed air off over that pressure. We always had to add a bit of air prior to the next outing, simply because we knew they bled off during the race, and as they cooled between races, the pressure naturally dropped.
Nitrogen is used in tires for two reasons:
1. Air compressors tend to allow moisture into the air stream. Moisture tends to yield a more sensitive pressure response to temperature (water can condense or vaporize with temperature changes).
2. Rubber is less permeable to nitrogen than it is to other components of air.
The inherent response of a gas pressure to temperature is, in fact, independent of the composition of the gas. That’s basic kinetic theory (from which the ideal gas law is derived). Filling with dry air would give the same result as filling with nitrogen as far as pressure response is concerned.