What you are describing is temperature gained due to kinetic heating of the aircraft as it moves through the air. The effect is not linear. It is neglible for speeds below Mach 0.3 or roughly 200KTS. Therafter the effect is increased as speed builds up.
Also a car temperature sensor doesn't hang off the car body, like a planes temperature probe does so I doubt you'll see the temperature display on your dash increase even if you managed to achieve a 250MPH cruise on the M1.