Assuming this is a B777-300ER-ULR.......with GE 90-115's...... At 351T - To the tonne rounded down MTOM
In general for MTOM operations, Flap 5 is limiting in this case. Flap 15 or 20 will be required depending on the runway and performance corridor. On 12L with QNH 1010, and 10kt headwind, Flap15/20 performance will allow a MTOM operation. As soon as the QNH goes below 1000 and the temperature above 40 degrees, Performance will not allow MTOM.
GE 90's have Takeoff Bump ( company option). In this case they can add circa 2-3t to the performance limited MTOM. Available -2000 to 3000 pressure alt and between 35 and 50 degrees.
However, the usual summer OMDB scenario is 30R, wind calm to 5kt headwind component - varying, 43 degrees, 998QNH. With these conditions, usually flap 15 from K15 intersection allows Max Structural Takeoff Mass.
The effects on aircraft performance of LLTI's are probably masked from the pilot noticing by the addition and subtraction of the Landing gear inner doors opening and closing during the gear up cycle. Two engines this is equivalent to roughly 2 degrees pitch.
The most noticeable inversion in these conditions is a 6-10degree inversion at around FL200, 10-15 kts gentle loss and a consequent loss of rate of climb at the aircraft noses down to regain commanded speed.