The amount of energy we are talking about is so tiny that obviously this is all academic.... however, and I have absolutely zero degrees in engineering, so am extremely likely to be mistaken here (ask my wife!), but it seems that if you are filling the pot from an outside source, it's not zero-sum.
During the winter the water from my well comes into the house at about 45F. You are bringing a big pot of cold into the house that wasn't there before. Energy that could have been used to raise/maintain the temperature in the house, is now being spent compensating for the cold being shed by that chilly water into your nice, warm house.
That said, there is always a teapot of water on my stove -- there's something about a cup of tea that goes so well with watching my secondaries do their thing.
During the winter the water from my well comes into the house at about 45F. You are bringing a big pot of cold into the house that wasn't there before. Energy that could have been used to raise/maintain the temperature in the house, is now being spent compensating for the cold being shed by that chilly water into your nice, warm house.
That said, there is always a teapot of water on my stove -- there's something about a cup of tea that goes so well with watching my secondaries do their thing.