One only flies little planes, real airplanes one might say as they have a wheel at the back. Getting off the ground is just an issue with these aircraft as big ones and there is bugger all instrumentation in them like you get on these computerised marvels of technology.
So when when departing from runways at high altitudes/temperatures I keep an eye on the indicated airspeed while on the runway. If I haven't reached 75% of 'takeoff speed' (get that from a book) by half way along the runway (get the length from a book) I stop. Very simple and it works. No idea whether that applies in airline operations but no reason to believe it wouldn't, it's basic newton law of motion. I suspect this has all been thought of by airlines' flight departments and they don't do anything silly in their published operations. Jetplanes are also somewhat better designed and overspecified than real planes and have a lot of redundancy built in.