An apparatus for manufacturing strengthened glass containers, and more particularly the construction and operation of a cooling tube mechanism in an apparatus for thermally strengthening glass containers in a glass container manufacturing line at a location intermediate the hot end and the cold end. Glass containers formed at an I. S. machine are conveyed through a special tempering Lehr that heats them uniformly to a high temperature that is short of temperatures at which they may become deformed. Subsequently, the glass containers are rapidly thermally strengthened in a cooling station in which the outer and inner surfaces including all areas of the glass containers are simultaneously cooled to a temperature below the Strain Point of the glass used in the glass containers, with the cooling tube mechanism being used to cool the inner surfaces of the glass containers.