As a mechanical engineer, I must take this opportunity to clear up a couple of points.
Firstly is the difference between absolute pressure and gauge pressure. The pressure value listed on the tyre is gauge pressure, which assumes an initial (empty) reading of zero. Absolute pressure is simply gauge pressure + atmospheric pressure at any given point. If the difference here is 3.6 psi atmospheric pressure, then the difference in gauge pressure would likewise be 3.6 psig.
Secondly is the relationship between pressure and temperature. Using the equation of PV=mRT that every student learns in chemistry 101, you can easily produce the equation P2=P1(T2/T1). (Tempeatures must be in absolute temperature, by adding 273 to degrees celsius, or 460 to degrees farenheit).
The blowout described by one person was likely caused mostly by temperature increase, due partly to friction on the tread, but mostly by heat from the brakes.
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