The temperature given was a TAT (Total Air Temperature) not what you would get sitting in a balloon holding a thermometer, that would be a Static Air Temperature. The TAT is what is actually sensed by an aircraft temperature probe. It is artificially high because of friction heating and the like as the aircraft rushes through the air. A moving aircraft might detect, for instance, a temperature of +20ºC when the actual temperature is +10ºC.
The temperature rise between SAT and TAT is proportional to the mach number. This means that, if we know the temperature rise in the sensing system, we can work backwards to find the Mach Number.