The speed of sound in gases is (roughly) proportional to the
square-root of the absolute temperature. Figures used the speed of
sound v_0 in air at 0℃ varies a bit in the range from 331.2 to 331.8
m/s perhaps. This gives the formula at absolute temperature T
v = sqrt(T/273.15)*v_0 m/s
For example, if the temperature of the air is 28℃, then T = 273.15+28
= 301.15 K (Kelvin). If v_0 is set to 331.5 m/s, then at 28℃, v =
sqrt(301.15/273.15)*331.5 = 348.1 m/s. Translated into pitches, this
is a change of 25.4 cents relative the speed 343 m*/s given above, or
a difference in tuning of about 6-7 Hz, or enough to hear the
instrument go out of tune. (But the temperature of the air varies
throughout the instrument - I just took a value to show how to
calculate v.)