An apparatus for use in controlling a temperature of an oblong-shaped molten glass-carrying vessel, such as a conduit for transporting the molten glass from one location to another location, by flowing a current through the vessel. The apparatus comprises a metal flange comprising a plurality of electrically-conductive rings that include an inner ring joined to the vessel's exterior wall and an outer ring surrounding the inner ring. The inner ring, for example, may include an outer perimeter that is substantially oblong. In some embodiments the inner ring comprises a notch that aids in making current density more uniform. In some examples the width of the inner ring, excluding the notch, does not substantially vary as a function of angular position relative to the vessel.