Really, we should create incentives for homes to be built with high thermal mass. Even without any sort of fancy direct heating or cooling of a thermal mass, it will store significant heat.

Welcome to traditional housing in Italy and probably elsewhere in the Mediterranean region. Thick stone walls even out the temperature swings through the day. Throw open the windows when the temperature is comfortable and close up when it gets too hot or cold depending on the season. This gets you quite far without any air-conditioning or heating.