A heating system for a vehicle includes a low-temperature circuit and a high-temperature circuit which can be operated independently of each other and in which a low-temperature cooler or a high-temperature cooler is arranged. The two cooling circuits are coupled to each other via two coupling points for the exchange of coolant, and have a common conduit section, which extends between the two coupling points and on which a heat exchanger is arranged for heating the passenger compartment. A respective heat exchanger is arranged in the two cooling circuits, namely a low-temperature heat exchanger or a high-temperature heat exchanger for receiving waste heat from a respective vehicle component. The cooling circuits can be switched between a cooling operation and a heating operation.