A drying cylinder for a paper-making machine comprises a cylinder barrel with end covers mounted on a hollow shaft. Steam for heating the cylinder can be introduced through an inlet at an end of the shaft. The steam passes through openings along the hollow shaft to heat the barrel. In order to reduce the risk of pollutants or condensate entering the annular space between the cylinder barrel and the hollow shaft, the openings in the hollow shaft are provided with tubular components which project into the interior of the hollow shaft. Either the tubular components themselves are shaped or a baffle plate is provided for blocking entrance of pollutants into the tubular components. A suction device removes condensate from the inside of the inner shaft.