Is thermal paste useful in copper / steel interface?
The dough will not resist heat and poorly conducts heat compared to a metal.
It would be better to solder with tin on the tube as for the gas boiler exchangers which avoids putting contiguous turns of copper which is expensive.
In addition, the exchanger must be insulated outside with glass wool and the pipes.
I would tend to put double the length is 2m with a T with vase collecting the soot and bistre and allowing to scrape and sweep often to keep a good exchanger !!