A method of controlling a speed of a gas turbine engine (10, 110) throughout a variation of output power thereof, the gas turbine engine including a gas generator spool (24, 124) and a power turbine spool (20, 120) rotating independently from one another, and a controller, the method comprising: controlling a rotational speed (Ng) of the gas generator spool (24, 124) according to a fixed relationship with respect to an air temperature measured outside of the gas turbine engine (10, 110) throughout the variation of output power, the rotational speed (Ng) of the gas generator spool (24, 124) being controlled by modulating an angle of variable inlet guide vanes (30, 130) located upstream of a compressor (14, 114) having at least one rotor (28, 128) rotating with the gas generator spool (24, 124), such that a corrected value (Ng') of the rotational speed of the gas generator spool (24, 124) remains at least substantially constant throughout the variation of output power, the corrected value (Ng') being determined based on the rotational speed (Ng) of the gas generator spool (24, 124) and the air temperature (θ) measured outside of the gas turbine engine (10, 110); and controlling a rotational speed (Np) of the power turbine spool (20, 120) to remain at least substantially constant throughout the variation of output power by modulating a fuel flow of the gas turbine engine (10, 110), wherein, in use, when the power demand increases on the gas turbine engine and the rotational speed (Np) of the power turbine spool (20, 120) starts to decrease, the controller, in response, commands the fuel flow to increase through a fuel control unit such as to bring the rotational speed (Np) of the power turbine spool (20, 120) back to the desired constant value, wherein as the fuel flow increases and the rotational speed (Ng) of the gas generator spool (24, 124) and its temperature-corrected value (Ng') start to increase, the controller, in response, commands inlet guide vanes to open through an inlet guide vane actuator such as to reduce the rotational speed (Ng) of the gas generator spool (24, 124) and bring the temperature-corrected value (Ng') back to the desired constant value while maintaining power. controlling a rotational speed (Ng) of the gas generator spool (24, 124) according to a fixed relationship with respect to an air temperature measured outside of the gas turbine engine (10, 110) throughout the variation of output power, the rotational speed (Ng) of the gas generator spool (24, 124) being controlled by modulating an angle of variable inlet guide vanes (30, 130) located upstream of a compressor (14, 114) having at least one rotor (28, 128) rotating with the gas generator spool (24, 124), such that a corrected value (Ng') of the rotational speed of the gas generator spool (24, 124) remains at least substantially constant throughout the variation of output power, the corrected value (Ng') being determined based on the rotational speed (Ng) of the gas generator spool (24, 124) and the air temperature (θ) measured outside of the gas turbine engine (10, 110); and controlling a rotational speed (Np) of the power turbine spool (20, 120) to remain at least substantially constant throughout the variation of output power by modulating a fuel flow of the gas turbine engine (10, 110), wherein, in use, when the power demand increases on the gas turbine engine and the rotational speed (Np) of the power turbine spool (20, 120) starts to decrease, the controller, in response, commands the fuel flow to increase through a fuel control unit such as to bring the rotational speed (Np) of the power turbine spool (20, 120) back to the desired constant value, wherein as the fuel flow increases and the rotational speed (Ng) of the gas generator spool (24, 124) and its temperature-corrected value (Ng') start to increase, the controller, in response, commands inlet guide vanes to open through an inlet guide vane actuator such as to reduce the rotational speed (Ng) of the gas generator spool (24, 124) and bring the temperature-corrected value (Ng') back to the desired constant value while maintaining power.