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Assumed is the temperature used to calculate the new, derated thrust.

When full engine power is not needed for take-off, the pilot can use reduced thrust for a number of reasons, including safety and economy ones. The way to do it is by calculating a number of factors (via the plane's flight computer) and estimating the max temperature at which the airplane could take-off from the given runway. You enter this temp to flight computer (the assumedtemp) to force the engine to produce less (derated thrust). And you still get to be safe, since you know from the tables that the airplane can actually land safely at this power setting.

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