For a given runway, the max aircraft TOGW decreases with increasing OAT. This is the result of two major factors:
1) Higher groundspeed required to reach V1, Vr etc. (Think a = F/m)
2) Reduced engine thrust available if OAT is above the flat rating limit.
Now if OAT = 10C and your performance-limited TOGW is 100t, but your actual TOGW is only 85t, you can look up the limiting OAT for a TOGW of 85t and call this your assumed or flex temperature (40C perhaps). At that OAT the engine power management would only permit say 90% of flat rated thrust. So it's within certified limits to use 90% thrust at your 85t weight.
But in fact you have MORE performance margin available, because the wing is flying in the 10C atmosphere, not 40C.
