Newton's law of cooling just says that your loss is going to be proportional to the temperature difference. But 1) the capacity of the battery is also proportio

Newton's law of cooling just says that your loss is going to be proportional to the temperature difference. But 1) the capacity of the battery is also proportional to the temperature difference, so the loss as a percentage of total energy stored should be roughly a constant. 2) If the application is home heating, you can't heat the home to a higher temperature than the battery itself, and you also can't easily group together the energy into a higher temperature. You would on the other hand want a high temperature for the heat to transfer quickly from the convection medium to the actual houses. So starting hot would make a lot of sense despite the downsides?