That is exactly why Aeromexico and Mexicana were the only customers to buy the DC-10-15.
This was basically a domestic DC-10-10 with the much larger engines from the DC-10-30. It could depart Mexico City in the height of summer with a full load of passengers.
For most normal aircraft the problem is known as the WAT Limit (Weight against Temperature). This basically means that although the runway is more than long enough for the aircraft to get airborne, the engines are not powerful enough at that height and temperature to enable the aircraft to climb.
If you don't have a DC-10-15 or similar then you have to reduce your payload and chuck the punters off!