With one
engine inoperative on a multi-engine aeroplane, the loss of directional control
is due to asymmetric thrust i.e. the turning-moment at high thrust settings.
Hence, if the temperature is high, the thrust will be less - reducing the
turning-moment at high power. Likewise, at high altitude, the air density is
reduced, once again resulting in less thrust being produced from the remaining
live engine(s), therefore resulting in a lesser turning-moment.