An apparatus for making a glass sheet including a forming apparatus, a transition member, and a heat transfer device. The forming apparatus forms a glass ribbon from a supply of molten glass. The transition member encloses the glass ribbon adjacent the forming apparatus, and defines an interior space through which the glass ribbon passes. The heat transfer device is disposed within the interior space, and comprises a tube and a fin. The tube defines an exterior surface and an interior passage. The fin projects from the exterior surface. With this construction, the heat transfer device functions to extract heat radiated by the glass ribbon while minimizing the formation of flow vortices.