> I think it makes more sense to put the heat pump between the "battery" and the building it's heating, so you draw less heat from the battery to supply a large

> I think it makes more sense to put the heat pump between the "battery" and the building it's heating, so you draw less heat from the battery to supply a large amount of heat to the building. That’s not how heat pumps work. They move heat from one medium to another - so using a heat pump to move one Joule from the battery to the house will lower the amount of heat in the batter by one Joule, same as if you use any other means. The efficiency gain that heat pumps provide when heating houses is that they essentially cool some medium (air, ground, water…) outside the building and move the heat into the building. Moving the heat uses less electricity than turning the electricity into heat via a resistive heating element. The outside medium gets warmed up by sun, or retains heat from a warmer season.