The last time I thought that Tester was wrong, it turned out to be me who was in error, but this time we are in my area of expertise, so I am willing to challenge with some degree of boldness.
That popular mechanics article contains a couple of erroneous, or at least poorly phrased, statements. As Texases stated, both nitrogen and oxygen exhibit ideal gas behavior. They both expand in direct proportion to the change in absolute temperature.
Absolute temperature, by the way, is measured in Kelvins or degrees Rankine. When I say that pressure rises in direction proportion to absolute temperature, that does not mean that heating a tire from 40F to 80F will double its pressure. 40F is 500R absolute, and 80F is 540R absolute.
The temperature increase from 40F to 80F is therefore 540/500 or an 8% increase in absolute temperature, which will result in an 8% increase in absolute pressure. To add yet another twist to this story, the pressure you read on your tire gauge is not the absolute pressure, it is the gauge pressure, or the difference between the measured value and the local atmospheric pressure.
EXAMPLE: At 32 psig gauge pressure, the absolute pressure is 32psig + 1 atmosphere, (~14.7 psia) or 46.7 psia. An 8% increase will result in a pressure of (1.08 * 46.7) = 50.4 psia absolute. Subtracting 14.7 psia for the atmosphere gives us a gauge pressure of 35.7 psig at 80F.
Folks who check their pressure at various temperatures can confirm that this is about the pressure change you would expect when heating from 40F to 80F. This relationship will hold whether the tire is filled with nitrogen, air, oxygen, argon, CO2, or any other gas that behalves as an ideal gas at standard conditions.
The problem with air, as noted previously, is that it tends to be wet. By compressing the air, the shop compressor drives up the dew point and dries the air pretty well, as anyone who has ever had the chore of bleeding the liquid water out of the compressor tank every night can attest. Sometimes, however, water condenses in the hose rather than the tank, and that water will go into your tire.
If you have liquid water in your tire, the pressure becomes much more unstable. Any change in temperature will change the liquid/vapor balance of the water in the tire. Water vapor takes up a LOT more space than liquid water. If even a tiny droplet of liquid water vaporizes, it takes up a lot of space in the tire, increasing the pressure in the tire, disproportionately to the change in absolute temperature. In a race car that is absolutely unacceptable. In your car it is not good.
Also, in cold weather, I would expect that ice inside the tire could cause tire imbalance.