The object of the invention is a system for transferring or removing heat from the air present in a room placed inside a building. The system is placed outside the building and is applied at a perimeter wall thereof. The system comprises a coil distributed over the entire surface of said wall and integrally connected to the latter by means of support bars. The coil is connected to a pump which makes heated or cooled water circulate therein, from a suitable respectively heating or cooling device, or alternatively capable of carrying out both functions, such as a reversible heat pump. The coil is inserted in a cement plaster layer externally covered with a first layer of material with high heat capacity in turn externally covered with a second layer of thermally insulating material. The water that circulates in the coil transfers or removes heat via irradiation to the air present in said room, through the perimeter wall. In a first variant of the system that is the object of the invention, the latter com- prises, in place of the coil, a carbon fiber resistor connected to a voltage or current generator that heats the resistor by Joule effect. In a second variant of the system that is the object of the invention, the latter lacks the cement plaster layer and comprises T-shaped beams for connecting to the perimeter wall of the layer with high heat capacity and of the thermally insulatin layer.