Method for operating a circulation system having a cooling device (12, 14) with an input port (12a, 14a) and an output port (12b, 14b) for the cooling of water and having a pipeline system with multiple branches comprising one or more partial sections with given thermal coupling to the surroundings and being connected by means of nodes, wherein one or more of the lines of the pipeline system are configured as a flow pipe (4, 5, 6), at least one as a single supply line connected to a tapping point, and at least one line configured as a circulation conduit connected to the flow pipe or pipes (4, 5, 6), with the steps - setting a water temperature at the output port (12b, 14b) to a value T a by means of the cooling device (12, 14) - setting a volume flow at the input port to a value V z characterized by the following steps - determining, in particular calculating, a temperature change of the water between the initial region and the end region according to a model of the axial temperature change for the first partial section connected to the output port (12b, 14b), starting from a temperature start value T MA * < T soll and a volume flow start value V z *, - determining, in particular calculating, a temperature change of the water between the initial region and the end region for each further given partial section according to the model of the temperature change, under the boundary condition that the water temperature in the initial region of the given partial section is equal to the water temperature in the end region of the partial section to which the given partial section is connected, and - selecting the value T a of the water temperature and the value V z of the volume flow at the output port (12b, 14b) such that, in the end region of each partial section, the water temperature is T ME < T soll and at the input port (12a, 14b) the water temperature is set at T b < T soll with T soll - T b < θ, where θ>0 is a given value. - setting a water temperature at the output port (12b, 14b) to a value T a by means of the cooling device (12, 14) - setting a volume flow at the input port to a value V z characterized by the following steps - determining, in particular calculating, a temperature change of the water between the initial region and the end region according to a model of the axial temperature change for the first partial section connected to the output port (12b, 14b), starting from a temperature start value T MA * < T soll and a volume flow start value V z *, - determining, in particular calculating, a temperature change of the water between the initial region and the end region for each further given partial section according to the model of the temperature change, under the boundary condition that the water temperature in the initial region of the given partial section is equal to the water temperature in the end region of the partial section to which the given partial section is connected, and - selecting the value T a of the water temperature and the value V z of the volume flow at the output port (12b, 14b) such that, in the end region of each partial section, the water temperature is T ME < T soll and at the input port (12a, 14b) the water temperature is set at T b < T soll with T soll - T b < θ, where θ>0 is a given value.