Abstract: A packing case for cooling compressors and other machinery is disclosed. A packing case includes an opening through which a movable machinery shaft may be inserted such that the packing case is mounted on the shaft. In an exemplary embodiment, the packing case contains at least one packing cup with channels through which a fluid coolant may flow. The channels form substantially parallel passageways along the length of the shaft that are spaced apart around the shaft circumference and series connected. The fluid coolant may be introduced through one or more inlet ports, circulate through the substantially parallel passageways of the at least one packing cup, and exit the packing case through one or more outlet ports. The fluid coolant may flow through the packing case in a single, continuous flow path or a split flow arrangement.