You get exactly 100% efficiency (as heating) at any temperature, since anything will be converted to heat anyway. Well, except in real systems you have exhaust

You get exactly 100% efficiency (as heating) at any temperature, since anything will be converted to heat anyway. Well, except in real systems you have exhaust temperature for CO2 etc going out of house, the lower the temperature the lower your heat loses. If you add some internal channels to chimney, you can absorb most of the heat back, making exhaust temperature very low therefore have low efficiency loss