A heating system (1) has a turbine (20) for burning a fuel to provide flue gas and electrical energy. A flue gas heat exchanger (25) receives the flue gas and uses it to heat water in three of stages. An air conduit (2) receives inlet air (3) and gases from secondary inlets (5, 26) from within the system to elevate the temperature in the main conduit (2) above ambient. An evaporator (8) recovering heat from the air flow of the main conduit, and provides energy via an evaporator coil to an air source heat pump ASHP (50). A water source heat pump WSHP (60) receives a water feed at an elevated temperature from the ASHP (50), and it cools the flue gas in a third heat exchanger stage (25(c)). Hence, WSW efficiency is high and it provides product water, as do the first and second stages of the flue gas heat exchanger (25)