Yes that's quite true.
The time limit on takeoff thrust is due to engine life, hence why it's 10 minutes instead of 5 for EO ops. At high EGTs engine life deteriorates non-linearly ie an increase of 5 degrees may reduce engine life 5 hours, but increase 5 degrees more and the life may reduce 500 hours (fictitious numbers by the way, merely to illustrate the point). The converse is also true, so at a high FLEX temperature the time limit would be greatly increased. However to actually calculate that on the line would be too complicated, and to be perfectly honest quite unnecessary. Good question though!
