There is a whole lot of misinformation about nitrogen filled tires. For those who appriciate the math and engineering analysis, here's a link to debunk the whole marketing myth:
To summarize, the FAA requires N2 filled tires on aircraft not due to expansion but to mitigate the chance of fire due to an overheated brake on landing. In addition, it is usually more convenient to drag a nitrogen bottle on a cart across the tarmac than to find a compressor and drag an air hose. Also, most aircraft tires are filled to 125 psi, which is at the high end for most small compressors.
As for the thermal expansion myth, it isn't due to air (which is already 80% nitrogen), it's due to water vapor. High pressure nitrogen bottles have considerably less water vapor than compressed air unless you have an outstanding drier in your compressor system. On the other hand, if you run through the math on the link I referenced, you'll find that for a normal, street-driven tire, the water vapor will make AT MOST a 0.5 psi difference as the tire is heated from room temp to 200 deg F. If you're worried about the water vapor in the air used to fill the tire, I'll again point out that the first thing you do when mounting a tire on a rim is to swab the beads. I'm willing to bet that puts way more water vapor inside the tire than any amount of compressed air.