Abstract: The present invention relates to a thermal shell for a building, apt to constitute a multi-layer system formed by three integral elements having, respectively, from the outside towards the inside: an external peripheral wall/casing with the function of thermal insulating wall; an interspace filled with air to be conditioned; an internal wall/casing with the function of heat-radiating wall/casing; comprising: a covering structure (10) positioned around the building (1), or part of said building (1), the covering structure (10) comprising, proceeding from the outside towards the inside of the building (1): a coating (11), an insulating layer (16) and an interspace (12); the interspace (12) containing air and forming a closed and isolated room with respect to the surrounding environment; means (13) of thermal conditioning of the air contained in the interspace, so that the shell defines an internal wall/casing.