The safety outflow device is provided in an end wall of a heatable godet and may be of a fusible type or pressure responsive type. The fusible safety device has fusible material which fills an outflow passage in a hermetic manner so that upon the occurrence of an excess temperature, the fusible material melts and permits exhaust of the vaporized medium. The pressure responsive safety device employs a burstable disc which bursts at a pressure corresponding to an overheated temperature so as to exhaust the heated medium.The safety devices serve as additional protection independently of manual and electrical means which may be provided.