The pressure in nitrogen filled tires will change when the temperature changes, just as it does with air filled tires, because nitrogen and oxygen respond to changes in ambient temperature in a similar manner. For example, when your
vehicle is parked it will lose a similar amount of pressure for every 10 degree change in temperature, whether the tires are filled with nitrogen or air.
The calculations for this change are based on the Ideal Gas Law. A good rule of
thumb is this: For every 10 F degree change in temperature, the pressure will change by 1.9%. If a tire is filled to 32 psi at a temperature of 75 F degrees and the temperature drops 10 degrees, the tire pressure will drop to 31.4 psi;
a difference of .6 psi. If a 100 psi tire is filled at 75 F degrees and the temperature drops 10 degrees, the tire pressure will drop to 98.1 psi; a difference of .9 psi.
These fluctuations will occur as the temperature rises and falls
no matter what the inflation gas. Fortunately, tire manufacturers are well aware of these conditions and design their tires and recommend their cold inflation pressure accordingly.
However, nitrogen does not contain the moisture and
other contaminants found in compressed air so, as you drive and the tires heat up, nitrogen filled tires will fluctuate less in temperature and pressure than air filled tires while driving. The bottom line is, you will still see pressure
changes with nitrogen but, overall, your tires will run cooler and at a more consistent pressure than if they were filled with air.
For more information please see the Effects of Temperature on Pressure
which shows the expansion rates of dry air or nitrogen, in both a truck and passenger tire, as the temperature increases. It also shows how the vapor pressure of water increases as temperature increases and includes a brief explanation.