The pressure rises in proportion to the temperature rise, in Kelvin. So, if you aired up your tires at room temperature (25C or 298K) then put the bike where the temperature got to 110 deg (43C or 316K), the rise in pressure is 316/298=1.06 times the original pressure. For a 100 PSI tire, you get only 6 psi added pressure.

Assuming you have healthy tires and tubes, you would need a much higher temp rise to cause a blowout. If you have some sort of defect in either, then anything is possible.