Heating system for motor vehicles including multi-function pump with axially displaceable impeller

A heating system in which a heat exchange arrangement operating in the manner of a heating member is thermally couplable via a hydraulic heat transfer circuit to a first heat source and to a second heat source, wherein a control arrangement is changeable over, in dependence on an operating state of a first pump allocated to said first heat source, between a first state, in which a heat transfer medium or at least a greater portion of said heat transfer medium is conducted over said first and second heat sources, and a second state, in which said heat transfer medium is conducted by a second, hydrodynamic pump, only or preponderantly over said second heat source, wherein said second pump has, axially displaceable in a pump housing, a radial impeller with radial impeller vanes arranged on one face of said radial impeller and a pump inlet arranged axially in front of said face and two radial pump outlets, mutually spaced apart in an axial direction of said radial impeller, and wherein a first pump outlet of said two radial pump outlets that is axially remote from said pump inlet communicates with an inlet side of said first heat source, and a second pump outlet of said two radial pump outlets that is axially nearer to said pump inlet communicates with an inlet side of said second heat source.