Air-conditioned building comprising: - a plurality of first walls configured to define together at least a first compartment, said first walls including first lateral walls, at least a first upper wall and at least a first lower wall, opposite said first upper wall, - a plurality of second walls located inside the first compartment and connected with each other to define together at least a second compartment, each of the second walls facing at least one of the first walls and distanced from the latter so as to define a continuous hollow space, closed with respect to said second compartment, and configured to contain a heat-carrying fluid, said second walls including second lateral walls, at least a second upper wall, and at least a second lower wall, disposed facing respectively said first lateral walls, first upper wall and first lower wall, - an air-conditioning apparatus configured to regulate the thermal state of said heat-carrying fluid, and comprising a conditioning unit located externally to said hollow space and a fluid-dynamic circuit that connects said hollow space to said conditioning unit with a closed-ring circuit, to make said heat-carrying fluid circulate in said hollow space and to provide thermal control of said second walls, characterized in that a first aperture is made in said at least one first upper wall or in said at least one second upper wall, and a second aperture is made in said at least one first lower wall, or in said at least one second lower wall, in that said fluid-dynamic circuit is connected on one side to said first aperture and on the other to said second aperture in order to connect the hollow space, with a closed circuit, to said conditioning unit, and in that said conditioning unit is served by a commutation member provided to invert the flow of heat-carrying fluid in the fluid-dynamic circuit, between the first aperture and the second aperture. - a plurality of first walls configured to define together at least a first compartment, said first walls including first lateral walls, at least a first upper wall and at least a first lower wall, opposite said first upper wall, - a plurality of second walls located inside the first compartment and connected with each other to define together at least a second compartment, each of the second walls facing at least one of the first walls and distanced from the latter so as to define a continuous hollow space, closed with respect to said second compartment, and configured to contain a heat-carrying fluid, said second walls including second lateral walls, at least a second upper wall, and at least a second lower wall, disposed facing respectively said first lateral walls, first upper wall and first lower wall, - an air-conditioning apparatus configured to regulate the thermal state of said heat-carrying fluid, and comprising a conditioning unit located externally to said hollow space and a fluid-dynamic circuit that connects said hollow space to said conditioning unit with a closed-ring circuit, to make said heat-carrying fluid circulate in said hollow space and to provide thermal control of said second walls, characterized in that a first aperture is made in said at least one first upper wall or in said at least one second upper wall, and a second aperture is made in said at least one first lower wall, or in said at least one second lower wall, in that said fluid-dynamic circuit is connected on one side to said first aperture and on the other to said second aperture in order to connect the hollow space, with a closed circuit, to said conditioning unit, and in that said conditioning unit is served by a commutation member provided to invert the flow of heat-carrying fluid in the fluid-dynamic circuit, between the first aperture and the second aperture.