Laundry drying appliance, - having a laundry drying chamber with a process air inlet opening and a process air outlet opening, which openings are interconnected by means of a process air duct to a process air circuit (2, 5), wherein - arranged in the process air duct are a capacitor for cooling process air emerging from the laundry drying chamber, a heater for heating previously cooled process air and a process air fan for recirculating the process air in the process air circuit (2, 5), further having - a heat pump (7, 9-12) with a drive, a first heat exchanger serving as the capacitor and a second heat exchanger serving as the heater, additionally having - a controllable closing device for optionally opening and closing a first air passage opening of the process air circuit (2, 5) and having - a second air passage opening, wherein the heater and the process air fan are arranged in the process air duct between the first air passage opening and the second air passage opening, and characterised in that the laundry drying appliance further has a controllable shut-off device for optionally opening and blocking the process air duct, wherein - the heater and the process air fan are arranged in the process air duct between the first air passage opening and the blocking device and - the closing device and the blocking device can be controlled such that simultaneously the closing device at least partially releases the first air passage opening and the blocking device at least partially blocks the process air duct, - the blocking device alternately at least partially releases or blocks the process air duct and the second air passage opening of the process air circuit is at least partially closed or released by means of a further closing device, - the closing device, the further closing device and the blocking device represent parts of an isolated air-guiding device (30, 31) and - the air-guiding device (30, 31) has a movable, in particular pivotable closing element, which has a first subregion serving as the closing device and a second subregion serving as the blocking device and the further closing device. - having a laundry drying chamber with a process air inlet opening and a process air outlet opening, which openings are interconnected by means of a process air duct to a process air circuit (2, 5), wherein - arranged in the process air duct are a capacitor for cooling process air emerging from the laundry drying chamber, a heater for heating previously cooled process air and a process air fan for recirculating the process air in the process air circuit (2, 5), further having - a heat pump (7, 9-12) with a drive, a first heat exchanger serving as the capacitor and a second heat exchanger serving as the heater, additionally having - a controllable closing device for optionally opening and closing a first air passage opening of the process air circuit (2, 5) and having - a second air passage opening, wherein the heater and the process air fan are arranged in the process air duct between the first air passage opening and the second air passage opening, and characterised in that the laundry drying appliance further has a controllable shut-off device for optionally opening and blocking the process air duct, wherein - the heater and the process air fan are arranged in the process air duct between the first air passage opening and the blocking device and - the closing device and the blocking device can be controlled such that simultaneously the closing device at least partially releases the first air passage opening and the blocking device at least partially blocks the process air duct, - the blocking device alternately at least partially releases or blocks the process air duct and the second air passage opening of the process air circuit is at least partially closed or released by means of a further closing device, - the closing device, the further closing device and the blocking device represent parts of an isolated air-guiding device (30, 31) and - the air-guiding device (30, 31) has a movable, in particular pivotable closing element, which has a first subregion serving as the closing device and a second subregion serving as the blocking device and the further closing device.