This post contains some good information, but some not so much. Let me explain as derived from my racing experience.
First - Nitrogen and virtually ALL other gasses expand at the same rate as temperature changes (Boyle's law). While some state that Nitrogen leaks more slowly that air, on a race car it's probably less than 1/2 hour from final inflation to the next pit stop. Not enough time to even be a consideration.
Second - Nitrogen in the cylinder is virtually dry.
Third - when a tire dealer fills your tire with Nitrogen, it already contains air and moisture from humidity. The air and humidity is not removed when they fill the tire.
Fourth - Racing tires can run up to 235 degrees during race. This causes the moisture if any to boil and turn to steam. Steam increases in volume by 1700 times it's volume of water. This increase causes a undetermined increase in pressure in the racing tire, and that's a no no for racing.
That is the reason that racing tires are filled with Nitrogen, but wait, there is more to the story. To eliminate the moisture in the racing tire, the air/moisture must be evacuated. This is NEVER done by your common tire dealer.
Here is what Goodyear publishes for their racing tire installation procedure
In humid areas such as Daytona they may purge 3 times, maybe only once in Las Vegas.