From the motor yachting world... If you can hold your hand on the header tank of a marine diesel engine cooling system for a few moments, but not more, then it's probably at about 80 deg C and the thermostat is functioning correctly. If you can't hold it, it's over 90, and if you can keep your grip for a while, it's probably under 70...
Therefore, any brake-related temperatures are well above the hand-test, but it is possible to get hold of hand-held thermometers for the purpose (the Bluecoat organisation had one circulating for a while).