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.