A foam extrusion assembly (10) having a melt region (20) and a heat extraction region (40) which extracts excess heat from a mixture of melted material pellets and blowing agent. The heat extraction region includes an elongate barrel (50) having an inlet (31) and an outlet (44), the inlet receiving the extrusion mixture for passage into the barrel wherein a heat extraction structure disposed with the barrel draws heat therefrom. An extrusion screw (60) is disposed in the barrel and includes a screw flight (64) structured to rotate within the barrel and urge the extrusion mixture towards the outlet of the barrel where a die (44) is disposed in order to form the finished product. The screw flight (64) includes a circulation channel (90) which receives quantities of the extrusion mixture upon rotation of the extrusion screw, thereby circulating the extrusion mixture towards the barrel for more effective and uniform cooling of the extrusion mixture to an extrudable temperature.