A heating system comprising: a district cooling grid used to satisfy comfort cooling demands, the district cooling grid having: a feed conduit conducting an incoming flow of a cooling fluid in the form of water, anti-freezing liquids or mixtures thereof, the incoming flow of cooling fluid having a first temperature in the range of 4-12 °C, a return conduit conducting a return flow of the cooling fluid, the return flow of 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 which cools 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 heating system of a building configured to heat the building and/or to heat tap water for the building, wherein the local heating system of the building is characterized in that it comprises: a heat pump having an inlet connected to the return conduit of the district cooling grid and an outlet connected to the feed conduit of the district cooling grid; and a pump arranged in the inlet (1 0a) or in the outlet of the heat pump, and configured to overcome the pressure difference between the return conduit and the feed conduit. a district cooling grid used to satisfy comfort cooling demands, the district cooling grid having: a feed conduit conducting an incoming flow of a cooling fluid in the form of water, anti-freezing liquids or mixtures thereof, the incoming flow of cooling fluid having a first temperature in the range of 4-12 °C, a return conduit conducting a return flow of the cooling fluid, the return flow of 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 which cools 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 conducting an incoming flow of a cooling fluid in the form of water, anti-freezing liquids or mixtures thereof, the incoming flow of cooling fluid having a first temperature in the range of 4-12 °C, a return conduit conducting a return flow of the cooling fluid, the return flow of 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 which cools 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 heating system of a building configured to heat the building and/or to heat tap water for the building, wherein the local heating system of the building is characterized in that it comprises: a heat pump having an inlet connected to the return conduit of the district cooling grid and an outlet connected to the feed conduit of the district cooling grid; and a pump arranged in the inlet (1 0a) or in the outlet of the heat pump, and configured to overcome the pressure difference between the return conduit and the feed conduit. a heat pump having an inlet connected to the return conduit of the district cooling grid and an outlet connected to the feed conduit of the district cooling grid; and a pump arranged in the inlet (1 0a) or in the outlet of the heat pump, and configured to overcome the pressure difference between the return conduit and the feed conduit.