What happens to the true airspeed if the outside air temperature increases during a flight at constant power and altitude?

When outside air temperature increases during a flight at constant power and altitude, the true airspeed will increase. This phenomenon is tied to the relationship between air density and temperature.

As the outside air temperature rises, the density of the air decreases. The aircraft operates under the principles of aerodynamics that dictate that with lower air density, the airplane's true airspeed—which is the speed of the aircraft relative to the surrounding air—must increase to maintain the same power output and lift.

In this scenario, assuming the aircraft is maintaining constant altitude and power settings, the increased true airspeed compensates for the reduced density of the air. The engines require less thrust to achieve the required lift due to the effects of thermal efficiency and reduced drag experienced in warmer, less dense air. Hence, the aircraft experiences an increase in true airspeed as the altitude is held constant, resulting in a higher performance output relative to the reduced air density.

Answering this question involves an understanding of aerodynamics, where temperature effects on air density directly influence the aircraft’s performance parameters.