A combined cooling and heating system comprising: a district cooling grid configured to be used to satisfy comfort cooling demands, the district cooling grid having: a feed conduit configured to conduct an incoming flow of a cooling fluid in the form of water, or water with an anti-freezing agent added thereto, the incoming flow of cooling fluid having a first temperature in the range of 4-12 °C, and a return conduit configured to conduct a return flow of the cooling fluid having a second temperature, the second temperature being higher than the first temperature, the second temperature being in the range of 10-18 °C; a district cooling plant configured to cool incoming cooling fluid of the return conduit from the second temperature to the first temperature, and a plurality of consuming cooling devices each configured to consume cooling of cooling fluid entering the consuming cooling device and thereby heating the cooling fluid, the heated cooling fluid being returned to the return conduit, wherein the cooling fluid is circulated in the district cooling grid by means of a pressure difference between the feed conduit and the return conduit, wherein the pressure in the feed conduit is higher than the pressure in the return conduit; a local cooling system being configured to absorb heat from a first building and comprising a heat exchanger having a heat exchanger inlet and a heat exchanger outlet; and a local heating system being configured to heat the first or a second building and comprising a heat pump comprising a first heat exchanger having a heat pump inlet and a heat pump outlet via which the heat pump is connected to a first circuit; wherein the heat exchanger inlet of the local cooling system is connected to the feed conduit of the district cooling grid; and wherein the heat pump inlet is connected to the return conduit of the district cooling grid and to the heat exchanger outlet. a district cooling grid configured to be used to satisfy comfort cooling demands, the district cooling grid having: a feed conduit configured to conduct an incoming flow of a cooling fluid in the form of water, or water with an anti-freezing agent added thereto, the incoming flow of cooling fluid having a first temperature in the range of 4-12 °C, and a return conduit configured to conduct a return flow of the cooling fluid having a second temperature, the second temperature being higher than the first temperature, the second temperature being in the range of 10-18 °C; a district cooling plant configured to cool incoming cooling fluid of the return conduit from the second temperature to the first temperature, and a plurality of consuming cooling devices each configured to consume cooling of cooling fluid entering the consuming cooling device and thereby heating the cooling fluid, the heated cooling fluid being returned to the return conduit, wherein the cooling fluid is circulated in the district cooling grid by means of a pressure difference between the feed conduit and the return conduit, wherein the pressure in the feed conduit is higher than the pressure in the return conduit; a feed conduit configured to conduct an incoming flow of a cooling fluid in the form of water, or water with an anti-freezing agent added thereto, the incoming flow of cooling fluid having a first temperature in the range of 4-12 °C, and a return conduit configured to conduct a return flow of the cooling fluid having a second temperature, the second temperature being higher than the first temperature, the second temperature being in the range of 10-18 °C; a district cooling plant configured to cool incoming cooling fluid of the return conduit from the second temperature to the first temperature, and a plurality of consuming cooling devices each configured to consume cooling of cooling fluid entering the consuming cooling device and thereby heating the cooling fluid, the heated cooling fluid being returned to the return conduit, wherein the cooling fluid is circulated in the district cooling grid by means of a pressure difference between the feed conduit and the return conduit, wherein the pressure in the feed conduit is higher than the pressure in the return conduit; a local cooling system being configured to absorb heat from a first building and comprising a heat exchanger having a heat exchanger inlet and a heat exchanger outlet; and a local heating system being configured to heat the first or a second building and comprising a heat pump comprising a first heat exchanger having a heat pump inlet and a heat pump outlet via which the heat pump is connected to a first circuit; wherein the heat exchanger inlet of the local cooling system is connected to the feed conduit of the district cooling grid; and wherein the heat pump inlet is connected to the return conduit of the district cooling grid and to the heat exchanger outlet.