A method to operate a laundry washing and/or drying appliance including • A treating chamber where laundry is introduced and treated with a process medium; • 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, said compressor including an electric motor, 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 medium; said method being characterized by comprising: • storing a plurality (j) of data couples, a first element of each data couple being function of a maximum current value i MAXj for the compressor electric motor current, and the second element of the couple being a corresponding function of a compressor maximum temperature value T MAXj associated to the maximum current value i MAXj of the first element, said plurality of data couples delimiting a predetermined safety work space for said compressor; • measuring substantially at the same time a temperature value T M representative of the temperature of said compressor and a current value i M representative of the current absorbed by said electric motor of said compressor while said heat pump is in operation; • comparing said measured temperature value T M and said measured current value i M with said plurality of data couples; and • limiting power supply to said compressor, which comprises: ▪ switching OFF the compressor electric motor; or ▪ adjusting a rotational speed of the compressor electric motor, if: ∘ there is a data couple (T MAXj*, i MAXj*) in said plurality for which | T MAXj * - T M | = min j | T M − T MAXj | and i M ≥ i MAXj* or ∘ there is a data couple (T MAXj*, i MAXj *) in said plurality for which | i MAXj* - i M |= min j | i M − i MAXj | and T M ≥ T MAXj*. • A treating chamber where laundry is introduced and treated with a process medium; • 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, said compressor including an electric motor, 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 medium; • storing a plurality (j) of data couples, a first element of each data couple being function of a maximum current value i MAXj for the compressor electric motor current, and the second element of the couple being a corresponding function of a compressor maximum temperature value T MAXj associated to the maximum current value i MAXj of the first element, said plurality of data couples delimiting a predetermined safety work space for said compressor; • measuring substantially at the same time a temperature value T M representative of the temperature of said compressor and a current value i M representative of the current absorbed by said electric motor of said compressor while said heat pump is in operation; • comparing said measured temperature value T M and said measured current value i M with said plurality of data couples; and • limiting power supply to said compressor, which comprises: ▪ switching OFF the compressor electric motor; or ▪ adjusting a rotational speed of the compressor electric motor, if: ∘ there is a data couple (T MAXj*, i MAXj*) in said plurality for which | T MAXj * - T M | = min j | T M − T MAXj | and i M ≥ i MAXj* or ∘ there is a data couple (T MAXj*, i MAXj *) in said plurality for which | i MAXj* - i M |= min j | i M − i MAXj | and T M ≥ T MAXj*. ▪ switching OFF the compressor electric motor; or ▪ adjusting a rotational speed of the compressor electric motor, ∘ there is a data couple (T MAXj*, i MAXj*) in said plurality for which | T MAXj * - T M | = min j | T M − T MAXj | and i M ≥ i MAXj* or ∘ there is a data couple (T MAXj*, i MAXj *) in said plurality for which | i MAXj* - i M |= min j | i M − i MAXj | and T M ≥ T MAXj*.