Almost all of the wood burning stoves that I have seen had a heat exchanger installed in the side of the fire box for hot water. water from the hot water tank circulated through the heat exchanger by convection.
A couple of old stoves that did not have the exchanger installed had provision for adding a heat exchanger.
As the combustion process consumed oxygen, make-up air infiltrated into the house.
On cold winter days, the moisture content of the make-up air could be extremely dry.
Without mitigation, the RH could drop to uncomfortable low levels.
It was always my understanding that the right-hand tank, furthest from the heat source, was intended to add moisture to the air and bring the RH up to a more comfortable level.
Is this suggestion compatible with your observations, John?
--------------------
Ohm's law
Not just a good idea;
It's the LAW!