The invention relates to a shaping apparatus for an extrusion system with at least one calibration die having a plurality of calibration units (31) disposed one after the other, having a calibration orifice (38) with a plurality of shaping surfaces (39 to 42) which come into contact with an article (6) fed therethrough, and end faces (43) spaced apart from one another with side faces (45 to 48) extending between them. At least one cavity is provided between at least two immediately adjacent calibration units (31). The calibration die is provided with means for dispersing heat. The calibration orifice (38) is provided with at least one continuous circulation passage (67) around a predominant part of and immediately adjacent to its circumference, having a separate inlet and outlet line (68, 69). The circulation passage (67) extends across a predominant distance of a thickness between the end faces (43) of the calibration unit (31), the circulation passage (67) being closed in the region of the two end faces (43).