The reason for the WAT (or MAT
) limitation and take-off limitations being stricter "hot and high" is the low air density. Not good for engine performance or aerodynamic performance. The aircraft has to reach a higher speed (true airspeed, that is) before it can support its weight by lift and there is less thrust available to reach that speed, so take-off performance is degraded. Then in the climb the thrust margin (thrust available compared to drag straight and level, i.e. the extra thrust available for climb) is lower, as there is less thrust. Thrust margin determines maximum angle of climb.