A system for air-conditioning air of a passenger compartment and for heat transfer with drive components of a motor vehicle. The system has a refrigerant circuit and a coolant circuit. The refrigerant circuit is formed with a compressor, a first refrigerant-coolant heat exchanger operated as a condenser/gas cooler, a refrigerant-air heat exchanger operated as an evaporator for conditioning supply air of the passenger compartment with an upstream expansion element, and a second refrigerant-coolant heat exchanger operated as an evaporator for heat transfer between a coolant for tempering the drive components of the motor vehicle and the refrigerant with an upstream expansion element, and with a bypass flow path around the heat exchangers operated as the evaporators on the low-pressure side. In addition to the first refrigerant-coolant heat exchanger, the coolant circuit has a coolant-air heat exchanger operated as a thermal heat exchanger for heating supply air of the passenger compartment.