A retrofitting appliqué for stepped application to a building wall construction. For external retrofitting, the system has an air barrier layer impermeable or semi-permeable for moisture, a ventilated air cavity used to modify temperature and/or remove water that may be coming from both sides or to modify the relative humidity of the ventilation air, a layer of thermal insulation, a composite material called Eco-Wrap with capillary active capability, in which a hydronic heating or cooling system may be located, and a surface finishing layer. For internal retrofitting, the system has an air barrier system arranged onto the wall of the building and separated from a layer of permeable or semi-permeable thermal insulation by a ventilated air gap. The layer of insulation, in turn, is in contact with a layer of Eco-Wrap. A permeable interior finishing layer that may also have capillary active performance is in contact with the Eco-Wrap. Methods for installing the retrofitting appliqué are also disclosed.