A tile, made for example of leather, having a first face, a second face, side edges and a plurality of holes that bring into communication first face with second face. In a lining made with such tiles like this, the holes lead the air from below to above the tiles. To improve further the air flow through the tile, on the second face a plurality of grooves are made that extend from a central zone up to the side edges of the tile. This way, an air path is formed between the lining and the floor leading the air to holes and then into the room at the side of first face. A favorable exchange rate through a floor lining made with them is obtained, combined with a heat exchanger embedded in the floor.