The Combined Gas Law states:
P1xV1/T1 = P2xV2/T2
P absolute pressure in atmospheres {(gauge pressure + 14.7)/14.7}
V volume
T temperature in degrees Kelvin
With an increase in pressure, the tire will stretch a little and the volume will increase. For this exercise, we will assume that the volume remains constant.
70 psig = 84.7 psia = 5.762 atm
84 psig = 98.7 psia = 6.714 atm
Assume T1 = 70F = 294.3K
Calculate the temperature, T2, required to raise the pressure from 70 psig to 84 psig.
T2 = T1 x P2/P1 = 294.3 x 6.714/5.762 = 342.9K = 158 F.
So it would take an 88F temperature rise to increase the pressure from 70 psig to 84 psig.
Now assume a 30F temperature rise from 70F to 100F.
Calculate the pressure rise.
Assume T2 = 100F = 310.9K
P2 = P1 x T2/T1 = 5.762 atm x 310.9/294.3 = 6.087 atm = 89.5 psia = 74.8 psig
So a temperature rise from 70F to 100F would increase the pressure from 70 psig to 75 psig.