Feels like nitpicket but: volume of air is in itself not a problem. There's not a whole lot of energy in air. The issue with heating/cooling is the surface area

Feels like nitpicket but: volume of air is in itself not a problem. There's not a whole lot of energy in air. The issue with heating/cooling is the surface area. With active heating/cooling, what really helps is better insulation. In Scandinavia and Germany people are insulating walls in new houses with 40 cm rockwool, or the equivalents thereof.