It wouldn't be certified to fly as a commercial aircraft if it couldn't complete a takeoff after V1 with one engine out. If the temperature were too high, the crew would have to leave off some weight (fuel, cargo, or passengers) to operate the aircraft within limits.
Actually, my initial speculation was that the pilots saw some sort of failure after V1, and tried to stop when they should have continued. That would put the aircraft off the end of the runway at (potentially) high speeds and could lead to the kind of impact/fire described. Incidentally, that's why there is a speed past which you continue the takeoff - it's better to get the plane into the air and circle to land then to run off the end of the runway and hit things on the ground.
The news media blamed all the MD-80's parked at LGA on "Global Warming" when it was "lowest bidder" parts failing in recently overhauled motors that was really causing the problem.
Either the pilots screwed up, the plane was way overweight or the failure was more catastophic than a simple inflight shut down.