Building system for the air-conditioning and heat supply of at least one building or part of a building via at least one heating network with at least one heat pump comprising an evaporator, a condenser and a refrigerant circulation system formed between the evaporator and the condenser, with at least one heat consumer, which is connected in a heat-transferring manner to the condenser of the heat pump on the condenser side via a heat-transfer-medium circulation system formed between the heat consumer and the condenser of the heat pump, and to heat-transfer-medium lines of the building system provided for connection to the heating network, wherein the building system comprises at least three heat-transfer-medium supply lines (11, 12, 13) at different temperature levels on the inlet side, of which one heat-transfer-medium supply line has a higher temperature level, one heat-transfer-medium supply line has a medium temperature level, and one heat-transfer-medium supply line has a low temperature level, characterized in that that the building system comprises controllable valves, via which the three heat-transfer-medium supply lines (11, 12, 13) can be controlled at the different temperature levels on the inlet side, wherein the respective heat-transfer-medium flow rate of the heat-transfer-medium supply lines (11, 12, 13) can be controlled via the controllable valves, that the evaporator is connected at least to the heat-transfer-medium supply line at the higher temperature level and to the heat-transfer-medium supply line at the medium temperature level on the inlet side, that the heat-transfer-medium supply line is connected to the heat consumer at the low temperature level, and that the building system has a valve branching the heat-transfer-medium supply line, via which the heat-transfer-medium supply line is connected to the condenser of the heat pump on the inlet side at the higher temperature level. wherein the building system comprises at least three heat-transfer-medium supply lines (11, 12, 13) at different temperature levels on the inlet side, of which one heat-transfer-medium supply line has a higher temperature level, one heat-transfer-medium supply line has a medium temperature level, and one heat-transfer-medium supply line has a low temperature level, characterized in that that the building system comprises controllable valves, via which the three heat-transfer-medium supply lines (11, 12, 13) can be controlled at the different temperature levels on the inlet side, wherein the respective heat-transfer-medium flow rate of the heat-transfer-medium supply lines (11, 12, 13) can be controlled via the controllable valves, that the evaporator is connected at least to the heat-transfer-medium supply line at the higher temperature level and to the heat-transfer-medium supply line at the medium temperature level on the inlet side, that the heat-transfer-medium supply line is connected to the heat consumer at the low temperature level, and that the building system has a valve branching the heat-transfer-medium supply line, via which the heat-transfer-medium supply line is connected to the condenser of the heat pump on the inlet side at the higher temperature level.