Er - no, the TAT probes measure just what they say Total Air Temperature.
They are mounted off the skin and in freestream, so they measure the same temperature as would a probe on the nose.
Somewhere near the nose (not exactly on it, as the aircraft flies with a small AoA) there will be a 'stagnation' streamline where the oncoming air is brought to rest. At this point the skin temperature will be equal to the stagnation temperature (TAT). Behind that it gets more complicated! The skin temperature would depend on SAT, local Mach No, local skin friction coefficient (Mach and Re dependent, so varies with distance from nose), amount of heat radiated into space (paint colour!) and the amount of structure available to conduct heat away from the skin into the fuel (so roughly varying with thickness/chord and fuel distribution perhaps?
OK, so the skin temperature at the stagnation point will be equal to TAT. This can be taken as the hottest part of the aircraft (behind it, the skin temperature will be less than the TAT).
The temperature shown in the top window of the flight deck gauge is TAT, with the legend 'TMO 128C' beneath it. So the aircraft was flown with reference to TAT, and provided TAT was no greater than 128C then the skin rearward of the stagnation point would be <128C?