It's always been my understanding that it eliminates the water vapor making the heat have less and more predictable effect on tire pressure.
Unless you are driving a race car or an airplane I don't think it's worth the trouble IMO
I found some more information I have listed and sourced below
It's not about the nitrogen. It's about reducing oxygen, water vapor
and other gases.
By reducing the percentage of oxygen, water vapor and other gases in
your tires from 22% to 7% or lower, your tires will maintain proper
pressure longer than if you use “plain old air.” For example, with 95%
nitrogen in your tires, they retain optimal pressure three to four
Fundamentally; air, oxygen and nitrogen will all behave exactly the
same in terms of pressure change for each 10 degrees of temperature
change. However temperature alone is not the whole story.
Ambient air contains moisture, nitrogen does not. If moisture is
present it contributes to a greater change in pressure simply because
at lower temperatures water condenses to become a liquid. The liquid
form of water occupies very little volume and contributes only a
negligible pressure to the tire. But at higher temperatures, such as
those in a running tire, water evaporates inside the tire and becomes
a gas which increases pressure in the tire.
Ambient air contains about 21% oxygen. Oxygen’s smaller molecular size
allows it to permeate through the rubber of the tire. By inflating
with nitrogen, which is much less permeable than oxygen, the pressure
changes due to oxygen loss are greatly reduced.
The racing industry is correct; nitrogen is more predictable. Because
nitrogen is dry it has no moisture to contribute extra pressure
changes with temperature. Because nitrogen permeates out much slower
than oxygen pressure changes due to that leakage are almost eliminated
compared with ambient air.
Let’s get a little deeper into the science. Keep in mind that the air
in your tires changes about 1psi for every 10 degree temperature
change. This means that a significant change in temperature will
create a significant change in your tire pressure. Here is a set of
Ideal Gas Law calculations showing the effects of a 10F degree
temperature change on truck and passenger tires. The two sets of data
represent different initial temperatures of 60F and 90F. This
demonstrates that the magnitude of the pressure fluctuation differs
depending on initial conditions but only slightly.