A cooling apparatus for a cylindrical member in linear motion comprises a tubular conduit through which the cylindrical member passes axially, an envelope surrounding the tubular conduit and forming therewith an annular chamber therebetween closed at its ends by an upstream wall and a downstream wall, respectively, cooling agent being introduced into the annular chamber. The tubular conduit is pierced radially by a plurality of a straight passages providing communication between the annular chamber and the internal space in the tubular conduit. These passages are located in planes perpendicular to and axially spaced along the longitudinal axis of the tubular conduit and are equally circumferentially spaced within each plane and angularly displaced with respect to the passages in the adjacent planes. Cooling agent passes through the passages radially inwardly and is drained from the internal space of the tubular conduit.