I would think that you may want a circulator to run constantly while burning wood if I'm understanding your explanation properly. Without convection you would have the opportunity for hot spots and steam to form and this could become dangerous. If your loop is large enough the excess heat would be dissipated in the house and not over heat the water heater and the pump could be turned off when the burner is out. Like an open circuit dhw heating system typically used with oil fired boilers. Flow controls could be used to slow the water flow enough to absorb the heat and allow it to heat the heater. This could be a multi purpose system to spread wood heat to distant rooms in the house even. It has great potential.
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