A gas turbine engine has an engine core, a fan arranged upstream of the engine core, and a hollow low-pressure shaft. The low-pressure shaft includes axially front and rear ends, wherein hot compressor air is applied to the axially rear end during operation. A valve is integrated into the interior of the low-pressure shaft, configured to open or close in accordance with the rotational speed of the low-pressure shaft, wherein the valve is closed from a predefined rotational speed and is open below this rotational speed, and wherein the valve, in the open state, allows hot compressor air to flow from the axially rear end of the low-pressure shaft to the axially front end of the low-pressure shaft and, in the closed state, prevents hot compressor air from flowing through the low-pressure shaft. A mechanism, when the valve is open, feeds hot compressor air outside of the fan disk.