I did not pay any more for air or nitrogen. It was an option from my dealer and at no additional change.
Since Atmospheric air is only 78% Nitrogen, 21% oxygen, the rest other gases, the 21% oxygen is what is fluctuating during the temperature changes. If you can get rid of the other 22% gases and put pure nitrogen in the tires, you will have a higher boiling and freezing point than Atmospheric Air. Dues to this, the tire psi will only change 1 psi during normal days. I keep my tires at 40 psi religiously and usually during normal highway driving in South Louisiana, they will go to 41 maybe 42 psi.
Nitrogen doesn't expand and contract as much as air with temperature. This is one of the major problems with air because when is cold or hot, for every 12 degrees change in temperature, the psi will increase or decrease respectively (i.e. deflate gate!!).
I have seen so much better wear with nitrogen vs air on my current tires compared to my last set.