Hi,
What you are missing is that the engine is flat rated.
Up to a certain OAT when you set toga you always get the same thrust. Above that temp the engine would normally be temperature limited so you would get a lower thrust to keep the ITT/TGT within limits.
So we are finding the OAT at which the ITT limited thrust would be sufficient for the actual weight and setting that thrust.
Now how we set that thrust is a different matter.
With a FADEC controlled engine we just lie to the FADEC about the OAT. It sets the thrust for that false(assumed) Temp.
However, as the real temp is lower and therefore the density higher the fadec has to make a correction to the thrust to take account of the temperature difference. So it needs to know the actual temperature as well as the assumed temperature to correct the thrust setting.