Methods of processing molten material comprising the step (I) of flowing molten material through an interior of a conduit (137) from a first station (131) to a second station (133) of a glass manufacturing apparatus and the step (II) of cooling the molten material within the interior of the conduit by passing a cooling fluid along an exterior of the conduit. The method further includes the step (III) of directing a travel path of the cooling fluid toward a vertical plane (319) passing through the conduit. In further examples, a glass manufacturing apparatus comprises a first station, a second station, and a conduit (137) configured to provide a travel path for molten material traveling from the first station to the second station. The glass manufacturing apparatus further comprises at least one baffle (323) configured to direct a travel path of cooling fluid toward a vertical plane (319) passing through the conduit.