For an ideal gas, the ratio of the pressures is equal to the ratio of the temperatures (assuming the no volume change or adding/subtracting gas). So

P1 / P2 = T1 / T2

The temperatures HAVE TO BE IN KELVIN. It just doesn't work without the temps in kelvin. 32 degrees F = 0 degrees C = 273 K. 100 degrees F = 38 degrees C = 311 K. This would be one hell of a temperature swing, but would increase the pressure by just under 14%. So that 100 psi tire would go up to 110 psi. Honestly I don't see how the temperature-induced pressure change alone can cause a blow-out when sitting on the bike doesn't. Your butt in the seat has to add more than 14% to the pressure in the tires, even when the weight is spread out over the whole volume of the tire.

Either there is water in the tire and the vapor pressure of the water is changing things (also unlikely; change in vapor pressure is only 6.5 kPa (1 psi) over temp range above) or the bike warming up makes the rubber more pliant and/or the rims expand a touch and a not-quite-properly-installed tire can slip and cause a blow out.