A simple water separator would not solve the problem. If it would, race car drivers wouldn’t have to underinflate their tires and wait for them to warm up to get full pressure. They would simply put in dry air. It may be possible to get all of the water out of air, but a simple separator won’t do that.
Did you read the first sentence of my response? OF COURSE nitrogen or any gas will expand with increasing temperature and hence increase pressure.
Charles’s law.
https://en.wikipedia.org/wiki/Charles’s_law
But if there is moisture (= water) in the gas it will add a non-linear component to the expansion.