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I'd say if all the tires say different than the gauge, I'd suspect the gauge.

 

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No mystery here - any gas's pressure is directly proportional to temperature (remember PV=nRT from HS physics?). So P=nRT/V. Tire volume can change but it turns out that for small pressure difference it doesn't make much of a contribution The temperature has to be measured in degrees (C or F is irrelevant, just be consistent) from absolute 0. Freezing 32F which is 273.15 above absolute 0, so 20F is 261 farenheit degrees above abs zero and 72 degrees is 313 farenheit degrees above abs zero. If we use 313 as the baseline temperature, the proportion 261/313 = .83 show that the pressure at 20F is only 83% of the pressure at 72F. So if your tire pressure at 72F is 38 psi it will only be .83 x 38 = 31.5 psi at 20F. Don't waste your time getting new sensors!
You're mixing up Fahrenheit and Kelvin, Kelvin uses the same degree intervals as Celsius, Fahrenheit is 1.8x the degree intervals (and zero is offset), so they are not straight interchangeable (only single exception is -40°, only place where F and C readings would match)

32°F is indeed 273.15K as absolute zero is 0K, but 0K is−459.67 °F, so 32 is 491.67 fahrenheit degrees above absolute zero, and 20°F would be 479.67 fahrenheit degrees above absolute zero, not 261 like you said.
 
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