Just out of curiosity, I did some back of the envelope calculations based on the numbers people have been throwing around in this thread.
Assumptions:
1. Tires originally inflated at 25 degrees C, since the op did not state
2. Ideal gas behavior (I know air isn't an ideal gas, but close enough to get a rough idea)
3. Volume and number of gas molecules are held constant (not strictly true in this case, but close enough)
If it is true, as one poster suggested that a properly installed tire can take 2x its rated pressure before blowing off, in this case (starting at 120psi), a temperature increase of 298 degrees C would be needed to reach this pressure. If ambient temperature increased by 10 degrees C (because it was a hot day), that still leaves an increase of 288 degrees C that would have to come from somewhere else.
I find it hard to believe that any amount of braking could generate that amount of heat, and if it did, you might have other things to worry about. Anyone know the melting point of butyl rubber?
It would seem more likely that:
A: The tire was not properly mounted (pinched tube, tire damage, other reason)
or
B: Tires can't really take 2x their rated pressure before blowing out.