Described herein is a packing box for mounting on a machinery shaft. In accordance with one aspect, the packing box housing defines a central opening for insertion of a movable machinery shaft with a hollow passageway surrounding the central opening to form a path for the flow of a fluid coolant. The passageway is provided with a fluid inlet port and a fluid outlet port opening onto the outer surface of the packing box housing, and it is formed by a single conduit or by a plurality of conduits obtained through additive manufacturing process and connected in series or in parallel to wound around the central opening.