I disagree with some although i will agree that consistent tire pressure is advantageous to an extent. I've never had or heard of problems where air temperature inside tires becomes a factor that must be dealt wtih and I live in Arkansas where temperatures routinely exceed 110 F and many days we are the hottest place in the world if you factor in humidity and temp.
Nitrogen's largest advantage is that your tires will not "oxidize" (the effect of exposure to oxygen) from the inside out. Nitrogen filled tires greatly reduces this threat as tires nowadays commonly last 60,000 miles which is plenty of time for the rubber compound to "dry-rot" from the inside out as well as outside in. In other words, your tires could wear out and become weak and still have plenty of tread depth left in them.
Youy hypothesis that you acheived greater fuel mileage is IMHGFO not possible (no shame in trying to improve though). There are many factory in fuel mileage such as wind direction, altitude, and average speed, and a pleathorea of others not mentioned.