Burner assembly for combustion of gaseous or liquid fuel to heat an industrial furnace, the process air in said industrial furnace having an amount of oxygen of 16% to 18%, the burner assembly having - a combustion chamber, - at least one main combustion air inlet for the supply of preheated combustion air into the combustion chamber, - a burner with at least one fuel feed and at least one air feed for supply of fuel and primary air into the combustion chamber, wherein the burner is positioned adjacent to a combustion zone of the combustion chamber such that the combustion air flowing into the combustion chamber through the main combustion air inlet is passing the burner in the combustion zone and is then deflected such that the flow of preheated combustion air and the smaller flows of fuel and primary air are flowing mainly in parallel from the burner to the furnace, - and a control unit, wherein (a) the control unit is adapted to control the supply of the fuel and the primary air from the fuel and air feed (7, 8) into the combustion chamber such that their exit velocity is higher than 150 m/s and such that the temperature of the primary air is in an ambient-like range of 20 °C to 100 °C, and (b) the control unit is further adapted to control the supply of preheated combustion air into the combustion chamber such that said preheated combustion air has an amount of oxygen of ambient air and being preheated to a temperature of 750° C to 1000° C. - a combustion chamber, - at least one main combustion air inlet for the supply of preheated combustion air into the combustion chamber, - a burner with at least one fuel feed and at least one air feed for supply of fuel and primary air into the combustion chamber, wherein the burner is positioned adjacent to a combustion zone of the combustion chamber such that the combustion air flowing into the combustion chamber through the main combustion air inlet is passing the burner in the combustion zone and is then deflected such that the flow of preheated combustion air and the smaller flows of fuel and primary air are flowing mainly in parallel from the burner to the furnace, - and a control unit, wherein (a) the control unit is adapted to control the supply of the fuel and the primary air from the fuel and air feed (7, 8) into the combustion chamber such that their exit velocity is higher than 150 m/s and such that the temperature of the primary air is in an ambient-like range of 20 °C to 100 °C, and (b) the control unit is further adapted to control the supply of preheated combustion air into the combustion chamber such that said preheated combustion air has an amount of oxygen of ambient air and being preheated to a temperature of 750° C to 1000° C. (a) the control unit is adapted to control the supply of the fuel and the primary air from the fuel and air feed (7, 8) into the combustion chamber such that their exit velocity is higher than 150 m/s and such that the temperature of the primary air is in an ambient-like range of 20 °C to 100 °C, and (b) the control unit is further adapted to control the supply of preheated combustion air into the combustion chamber such that said preheated combustion air has an amount of oxygen of ambient air and being preheated to a temperature of 750° C to 1000° C.