Flex or assumed temp TO - In its simplest form there are two elements. For a given runway, increasing ambient temp. hurts your TOGW capability for two reasons:
1) Higher TAS (inertial speed) is required to achieve V1, Vr etc., which are IAS values.
2) Engine thrust available is less at higher ambient temp.
Playing this game backwards, if you are planning a takeoff on a relatively cool day, at a lesser TOGW, you can ask "What is the hottest ambient I can stand and still be legal at this TOGW?"
Once this temperature is known, you can set thrust equivalent to what the engines could produce on the hot day (i.e. reduced thrust), and have assured performance no worse than the certified hot day value. (Remember, the wing is still flying in cooler air)
OK?