A heating system configured to be connected to a heating distribution system of a building, the heating system comprising: a heat pump arrangement configured to heat a fluid; a stratified heat storage device configured to store the fluid at differentiated temperatures, wherein the heat storage device is arranged in fluid connection with the heat pump arrangement; a mixing arrangement arranged in fluid connection with the heat storage device and the heating distribution system; and a control device for controlling the heating system; wherein the heat pump arrangement is configured to supply outgoing fluid to the heat storage device and to subtract ingoing fluid from the heat storage device, and the heat storage device is configured to supply fluid via the mixing arrangement to the heating distribution system and to receive returning fluid from the heating distribution system, wherein the mixing arrangement is configured to subtract fluid from the heat storage device and to regulate the temperature of the fluid entering the heat distribution system, wherein the heat pump arrangement is configured to supply the outgoing fluid to the heat storage device at an outgoing temperature (T Out) of at least 55°C, wherein an ingoing temperature (T In) of the ingoing fluid subtracted from the heat storage device by the heat pump arrangement is at least 20°C lower than the outgoing temperature (T Out) of the outgoing fluid from the heat pump arrangement, the heating system further comprises a bypass arrangement for bypassing the heat storage device during start up of the heat pump arrangement, characterized in that $ the mixing arrangement is configured to control the return of the returning fluid from the heating distribution system based on temperature values of the returning fluid provided by a returning fluid temperature sensor arranged downstream the heating distribution system, in order to ensure that the temperature difference within the heat storage device is at least 10°C, $ and in that the heat storage device comprises at least one stratifier inlet device for distribution of returning fluid from the heating distribution system within the heat storage device. a heat pump arrangement configured to heat a fluid; a stratified heat storage device configured to store the fluid at differentiated temperatures, wherein the heat storage device is arranged in fluid connection with the heat pump arrangement; a mixing arrangement arranged in fluid connection with the heat storage device and the heating distribution system; and a control device for controlling the heating system; wherein the heat pump arrangement is configured to supply outgoing fluid to the heat storage device and to subtract ingoing fluid from the heat storage device, and the heat storage device is configured to supply fluid via the mixing arrangement to the heating distribution system and to receive returning fluid from the heating distribution system, wherein the mixing arrangement is configured to subtract fluid from the heat storage device and to regulate the temperature of the fluid entering the heat distribution system, wherein the heat pump arrangement is configured to supply the outgoing fluid to the heat storage device at an outgoing temperature (T Out) of at least 55°C, wherein an ingoing temperature (T In) of the ingoing fluid subtracted from the heat storage device by the heat pump arrangement is at least 20°C lower than the outgoing temperature (T Out) of the outgoing fluid from the heat pump arrangement, the heating system further comprises a bypass arrangement for bypassing the heat storage device during start up of the heat pump arrangement, the mixing arrangement is configured to control the return of the returning fluid from the heating distribution system based on temperature values of the returning fluid provided by a returning fluid temperature sensor arranged downstream the heating distribution system, in order to ensure that the temperature difference within the heat storage device is at least 10°C, $ and in that the heat storage device comprises at least one stratifier inlet device for distribution of returning fluid from the heating distribution system within the heat storage device.