In hot/high conditions, the air being thinner, engine performance (as with car engines) becomes compromised therefore slowing the acceleration and extending the point where lift off speed is attained (take off distance required).
Wookey: You are absolutely on the right track, however, as Bergerie 1 says:
Even the VC10 made one hold one's breath on occasions
Any airplane, except one with electric motors, will eventually run out of steam as Weight/Altitude/Temperature increase. There's no substitute for horsepower!!
That's also one reason why you're starting to see electrically powered UAV's.
TC