Abstract: An air-conditioning device for air-conditioning a passenger compartment is provided. The air-conditioning device includes a cooling element for cooling air, an air duct downstream of the cooling element for guiding the air, a heating element downstream of the air duct for warming the air, a mixing zone downstream of the heating element, and multiple air outlets for discharging multiple partial air streams from the mixing zone into different regions of the passenger compartment. An additional cold air bypass is formed which is guided past the heating element for supplying additional cold air downstream of the heating element. As a result, the air-conditioning device in operation is particularly efficient and simultaneously simple in design and particularly cost-effective. Furthermore, the invention provides a method for operating the air-conditioning device.