Using the combined gas law:



Due to the nature of the tire we can assume the volume of the tire will be very close to the same with a slight increase in pressure. In other words it may stretch slightly but the tire cords prevent much change. So we will set V1=V2. Even if the volume did increase it would only lower the pressure change with temperature.

Assuming it was a nice brisk morning at 40°F when the tire was filled or 278°Kelvin. Also assuming that the tire is left in a nice hot car at 125°F or 325°Kelvin with an initial round number inflation pressure of 50PSI. The pressure could be converted to pascals but it does not matter here.

This yields a pressure increase in the tire of 8PSI to 58PSI, clearly not enough to blow a tire. Or roughly about 1PSI for every 6°C or 10°F. Please punch thru the calculations yourself.

Pressure or temp conversions can be found here:
http://www.unitsconverter.net/

The reason a tire would blow would be road debris, tire/rim damage, faulty rim, tire/tube mismatch, tire/tube shift due to under-pressure or braking, or UV damage to the tube at the valve stem.