Loki Tims, have you thought that an open fire is far less efficient than a closed fire, with the right amount of air supply, and heat "concentration" ?
https://www.tfswoodstoves.co.uk/WhyWoodstove.aspx?id=11
Open
wood fires are about 20% efficient. A rocket, can be in the range of 90%
Heat recovery, and ambient air loss is also at play.
Heat recovery in an open hearth, might be in the order of 10% of the heat recovered. And if the fumes are cold, this is not due to only the fumes going up the chimney, but because of air dilution. The chimney sucks huge amounts of hot air, with your smoke. So you're cooling the home, to heat the home.
This is why stoves have been invented, and refined.