An appliance for drying laundry including a drying-air moisture-condensing system comprising a heat pump system ( 215,220,225) with a variable-output compressor, and at least one drying air variable-speed fan for promoting the recirculation of the drying air, the appliance being adapted to perform at least one laundry drying cycle in: at least a first drying mode wherein the compressor is driven to a first compressor mode having a first compressor power consumption course and/or a first compressor rotational speed course and/or a first frequency course of the supply current/voltage of the compressor motor and the fan is driven to a first fan mode having a first speed course, and at least a second drying mode wherein the compressor is driven to a second compressor mode comprising a second compressor power consumption course and/or a second compressor rotational speed course and/or a second frequency course of the supply current/voltage of the compressor motor and the fan is driven to a second fan mode having a second speed course, wherein for at least a portion of the drying cycle, a compressor power consumption and/or a compressor rotational speed and/or a frequency of the supply current/voltage of the compressor of the second compressor mode is/are higher than the one/s of the first compressor mode and the speed of the second fan mode is higher than the speed of the first fan mode, so as to shorten the laundry drying cycle, characterized by comprising a control unit adapted to automatically activate the second drying mode when a user actuates a command input means of a user interface of the appliance, and at least one Joule-effect heater that, in the second drying mode, is kept energized for at least an initial portion of the drying cycle for boosting the heating of the drying air and is kept de-energized when the compressor is driven in the second compressor mode. at least a first drying mode wherein the compressor is driven to a first compressor mode having a first compressor power consumption course and/or a first compressor rotational speed course and/or a first frequency course of the supply current/voltage of the compressor motor and the fan is driven to a first fan mode having a first speed course, and at least a second drying mode wherein the compressor is driven to a second compressor mode comprising a second compressor power consumption course and/or a second compressor rotational speed course and/or a second frequency course of the supply current/voltage of the compressor motor and the fan is driven to a second fan mode having a second speed course, wherein for at least a portion of the drying cycle, a compressor power consumption and/or a compressor rotational speed and/or a frequency of the supply current/voltage of the compressor of the second compressor mode is/are higher than the one/s of the first compressor mode and the speed of the second fan mode is higher than the speed of the first fan mode, so as to shorten the laundry drying cycle, characterized by comprising a control unit adapted to automatically activate the second drying mode when a user actuates a command input means of a user interface of the appliance, and at least one Joule-effect heater that, in the second drying mode, is kept energized for at least an initial portion of the drying cycle for boosting the heating of the drying air and is kept de-energized when the compressor is driven in the second compressor mode.