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?
TAT varies with the square of Mach Number and SAT, and although all temperatures for calculation purposes are obviously ABSOLUTE temperature, they are 'converted back' to
°C here. So shown below are a range of TATs shown at four different Mach numbers and three specific SATs (or OAT if you prefer). Altitudes can be assumed as being in the lower stratosphere (ie. above tropopause) and ISA relates to International Standard Atmosphere. ISA is of course -56.25
°C, ISA -5 is -61.25°C and ISA +5 is -51.25°C.
MACH 0.5.ISA -5: TAT = -50.6°C. ISA: TAT = -45.3°C. ISA +5 TAT = -40°C
MACH 1.0. ISA -5: TAT = -18.5°C. ISA: TAT = -12.5°C. ISA +5 TAT = -6.5°C
MACH 1.5. ISA -5: TAT = 34.8°C. ISA: TAT = 42°C. ISA +5 TAT = 49.3°C
MACH 2.0. ISA -5: TAT = 109.5°C. ISA: TAT =118.6°C. ISA +5 TAT = 127.6°C
Hopefully it all makes a little more sense with some 'real' numbers. You can see that as Mach Number increases the gap between SAT and TAT increases hugely. The Mach 2, ISA +5 case was particularly significant for Concorde, as it breached the 127°C/400°K airframe temperature limit (TMO) and Mach Number would therefore be automatically reduced by the autopilot. (An overspeed warning would be generated at TMO +7 (134.°C). Fortunately sustained ISA +5 or above conditions were relatively rare over the North Atlantic but not unheard of either.