A method to operate a laundry drying appliance including: • a treating chamber where laundry is introduced and treated with process air; • a heat pump system having a refrigerant circuit in which a refrigerant can flow, said refrigerant circuit including a first heat exchanger where the refrigerant is cooled off, a second heat exchanger where the refrigerant is heated up, a compressor to pressurize and circulate the refrigerant through the refrigerant circuit, and a pressure-lowering device ; said first and/or second heat exchanger being apt to perform heat exchange between said refrigerant flowing in said refrigerant circuit and said process air; • a selector adapted to select alternatively one of a plurality of drying programs, each drying program including a main drying phase; said method comprising: • setting a first limit temperature value representative of the limit temperature of the compressor ; • setting a second limit temperature value representative of the limit temperature of the compressor ; • selecting a drying program among the plurality and starting its drying phase; • sensing an operating parameter representative of the humidity of the laundry in the treating chamber ; • measuring a temperature value representative of the temperature of said compressor ; • selecting the first limit temperature value for a first plurality of values of the sensed operating parameter representative of the humidity of the laundry during the drying phase; • selecting the second limit temperature value for a second plurality of values of the sensed operating parameter representative of the humidity of the laundry during the drying phase; and • limiting power supply to or switching off said compressor if the measured temperature value is higher than the first or the second limit temperature value, depending on which one is selected when the measured temperature value exceeds the limit temperature value. • a treating chamber where laundry is introduced and treated with process air; • a heat pump system having a refrigerant circuit in which a refrigerant can flow, said refrigerant circuit including a first heat exchanger where the refrigerant is cooled off, a second heat exchanger where the refrigerant is heated up, a compressor to pressurize and circulate the refrigerant through the refrigerant circuit, and a pressure-lowering device ; said first and/or second heat exchanger being apt to perform heat exchange between said refrigerant flowing in said refrigerant circuit and said process air; • a selector adapted to select alternatively one of a plurality of drying programs, each drying program including a main drying phase; • setting a first limit temperature value representative of the limit temperature of the compressor ; • setting a second limit temperature value representative of the limit temperature of the compressor ; • selecting a drying program among the plurality and starting its drying phase; • sensing an operating parameter representative of the humidity of the laundry in the treating chamber ; • measuring a temperature value representative of the temperature of said compressor ; • selecting the first limit temperature value for a first plurality of values of the sensed operating parameter representative of the humidity of the laundry during the drying phase; • selecting the second limit temperature value for a second plurality of values of the sensed operating parameter representative of the humidity of the laundry during the drying phase; and • limiting power supply to or switching off said compressor if the measured temperature value is higher than the first or the second limit temperature value, depending on which one is selected when the measured temperature value exceeds the limit temperature value. <EOS>