I often make use of the Engineering Toolbox when I have some problem to solve.
Since I'm trying to heat water with wood, I want to find out how much wood I'm likely to need. It appears that perfectly dry wood contains 7000 BTUs per pound. One btu is the amount of heat required to raise one pound of water by one degree Fahrenheit.
Let's go with 10 gallons of water. I will calculate the amount of weight in the water and burn one pound of fuel to see how much hotter it could become in perfect conditions. Let's start with well water that is 50 degrees Fahrenheit. I'll use the American gallons. Somebody, somewhere in history, needs a good slap for making two different gallons.
An American gallon weighs 8.34 pounds. 10 gallons weighs 83.4 lb. A pound of dry wood contains 7000 BTUs. 7000÷ 83.4=83.93 ----- So, we can raise our 50 degree water by roughly 84 degrees. 84+50=134 In perfect conditions, one pound of wood is needed to have a hot bath. In real world conditions it may take 2 or 3 pounds, but not 20.