The whole concept is based on the typical airline situation where the fuel+payload are well below what the aircraft will carry out of a given runway, or (viewed another way) there's excess runway available for the given TOGW.
ANY engine has less power/thrust available as OAT increases, because of temperature and/or rpm limits. This is regulated by the engine control system, or by power management charts on older engines.
If an engine is flat rated to 30º C, it means that while power/thrust decreases above this OAT, but is not permitted to increase (ie held flat) below that temp.
So if the airplane has excess performance at a temp. of (say) 15º C, we look up the max OAT for which the airplane would be legal for this runway, and that might be 38 or 43º C. So we assume that temp for the TO planning.
Advantages: 1) the engine is running no harder than it needs to; and 2) the airplane wing is flying in air cooler than the assumed temp (meaning a lower groundspeed for each IAS).
But there are operational restrictions on Assumed Temp. method (no contaminated runway, etc.) so Derated performance sections in the AFM are provided.