Thermal shell for a building, apt to constitute a multi-layer system formed by three integral elements comprising, 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; including alternatively - a covering structure positionable externally around an existing building, or part of an existing building, said covering structure being composed of panels comprising, proceeding from the outside towards the inside of the building: a coating, an insulating layer and defining an interspace around external walls of said building; said external peripheral wall/casing with the function of thermal insulating wall being formed by said coating and said insulating layer; said internal wall/casing with the function of heat-radiating wall/casing being formed by said external walls of the building; or - a covering structure applicable as external walls in a building, said covering structure being composed of panels having a multilayer structure that includes, from the outside towards the inside of the building, a coating or structural layer, an insulating layer, an interspace and a layer consisting of a heat radiating cladding; said external peripheral wall/casing with the function of thermal insulating wall being formed by said coating or structural layer and said insulating layer; said internal wall/casing with the function of heat-radiating wall/casing being formed by said layer consisting of a heat radiating cladding; said internal wall/casing with the function of heat-radiating wall/casing being in contact with the confined environments destined to the housing functions; said interspace (12, 23) containing air and forming a room, which is closed with respect to the surrounding environment inside the buiding, without any passage for said air from said interspace to inhabited confined environments of said building and which is closed and thermally isolated with respect to the surrounding environment outside the buiding, said room being apt to optimize the natural descending/ascending air flows; said thermal shell additionally comprising means of thermal conditioning of the air in said interspace (12, 23). - a covering structure positionable externally around an existing building, or part of an existing building, said covering structure being composed of panels comprising, proceeding from the outside towards the inside of the building: a coating, an insulating layer and defining an interspace around external walls of said building; said external peripheral wall/casing with the function of thermal insulating wall being formed by said coating and said insulating layer; said internal wall/casing with the function of heat-radiating wall/casing being formed by said external walls of the building; or - a covering structure applicable as external walls in a building, said covering structure being composed of panels having a multilayer structure that includes, from the outside towards the inside of the building, a coating or structural layer, an insulating layer, an interspace and a layer consisting of a heat radiating cladding; said external peripheral wall/casing with the function of thermal insulating wall being formed by said coating or structural layer and said insulating layer; said internal wall/casing with the function of heat-radiating wall/casing being formed by said layer consisting of a heat radiating cladding; said internal wall/casing with the function of heat-radiating wall/casing being in contact with the confined environments destined to the housing functions; said interspace (12, 23) containing air and forming a room, which is closed with respect to the surrounding environment inside the buiding, without any passage for said air from said interspace to inhabited confined environments of said building and which is closed and thermally isolated with respect to the surrounding environment outside the buiding, said room being apt to optimize the natural descending/ascending air flows; said thermal shell additionally comprising means of thermal conditioning of the air in said interspace (12, 23).