There was much speculation about using water for heat storage and temp. moderation back in the 70s and early 80s when I was both thinking about and building my cottage. The info' was everywhere, it seemed. Along with buried stores of stones, massive blocks of concrete, etc. Anything that gets heated will later provide heat back into the air around it. Eventually.
So, I knew a number of people who tried the water storage ideas, some of them. None still have the things set up, whatever they were. The results were disappointing, to be blunt. Barrels had stratification which seemed to decrease efficiency [according to those who used them, anyway]. Even painted flat black, they never heated up as much [or even near as much] as calculated. Plus, shorter daylight spells available when the heat is wanted [winter] kept the water from ever getting very warm, so there was never much heat to add back into the greenhouse or room. Plus, the space those barrels took, the physical presence, was unfortunate...lots of lost square footage for living in or growing plants.
One couple up here tried the gallon-milk-jug thing, hundreds of them stacked along a wall in the greenhouse, in full sun [filtered thru the glazing, of course] and filled with black-dyed water. It has been too long for me to remember specifics except to say they eventually got rid of all the jugs and considered it a failure.
I watched all these things and never tried them myself, plus my own place is small and I have limited space to sacrifice.
Reading magazine articles and etc. back then, some experimenters decided that the answer was to have a pump which would stir the water, eliminate stratification. More technology, plumbing, electricity, no longer a passive system. I don't recall those results. Heating the water in storage with wood or whatever fuel would help but the question is would the gain be increased; in other words, one would be hoping to get more BTUs or more usable BTUs from the same fire...begins to make no sense to me. If it requires more fuel to get more storage, is there a net gain.... Well, if one is hoping to spread out the heat available throughout the day and night, then maybe.
But experimenting is fine. My observations of the others around here trying these things is that the problem was getting the water heated up sufficiently to have the heat to put back in the first place. At least, doing so with "free" and hassle-free solar gain. If one must use propane or electricity or wood to heat up the water in storage, well.....