Arrangement for the heat supply of a building comprising - an expansion valve for expanding a refrigerant, - an evaporator for evaporating the expanded refrigerant, - an internal heat exchanger for superheating the evaporated refrigerant, - a compressor for compressing the superheated refrigerant, - a first heat exchanger for transferring the heat of the compressed refrigerant to a fluid circuit, - an inlet leading into the evaporator for a heat source fluid, preferably brine, - a first device for determining a first temperature, - a second device for determining a second temperature, - a third device for determining a third temperature, and - wherein the third temperature is a temperature of the refrigerant between the internal heat exchanger and a refrigerant inlet of the first heat exchanger, preferably between the compressor and the refrigerant inlet of the first heat exchanger, characterised by - an auxiliary controller for controlling the expansion valve so that a difference between the first temperature and the second temperature corresponds to an auxiliary setpoint, - a main controller which adjusts the auxiliary setpoint based on the third temperature, and - a second heat exchanger connected in series to the first heat exchanger for transferring the heat of the refrigerant to the fluid circuit downstream of the first heat exchanger, - wherein the refrigerant downstream of the second heat exchanger and upstream of the expansion valve is useful for superheating the evaporated refrigerant in the internal heat exchanger, - wherein the first temperature is a temperature of the heat source fluid in the inlet, and - wherein the second temperature is a temperature of the refrigerant between the expansion valve and the evaporator. - an expansion valve for expanding a refrigerant, - an evaporator for evaporating the expanded refrigerant, - an internal heat exchanger for superheating the evaporated refrigerant, - a compressor for compressing the superheated refrigerant, - a first heat exchanger for transferring the heat of the compressed refrigerant to a fluid circuit, - an inlet leading into the evaporator for a heat source fluid, preferably brine, - a first device for determining a first temperature, - a second device for determining a second temperature, - a third device for determining a third temperature, and - wherein the third temperature is a temperature of the refrigerant between the internal heat exchanger and a refrigerant inlet of the first heat exchanger, preferably between the compressor and the refrigerant inlet of the first heat exchanger, - an auxiliary controller for controlling the expansion valve so that a difference between the first temperature and the second temperature corresponds to an auxiliary setpoint, - a main controller which adjusts the auxiliary setpoint based on the third temperature, and - a second heat exchanger connected in series to the first heat exchanger for transferring the heat of the refrigerant to the fluid circuit downstream of the first heat exchanger, - wherein the refrigerant downstream of the second heat exchanger and upstream of the expansion valve is useful for superheating the evaporated refrigerant in the internal heat exchanger, - wherein the first temperature is a temperature of the heat source fluid in the inlet, and - wherein the second temperature is a temperature of the refrigerant between the expansion valve and the evaporator.