A foam extrusion assembly having a melt region wherein a plurality of material pellets are melted and mixed by a mixing assembly with a blowing agent introduced via an agent addition assembly. The foam extrusion assembly further includes a heat extraction region structured to extract excess heat from the mixture of melted material pellets and blowing agent such that the mixture achieves an extrudable temperature. The heat extraction region includes an elongate barrel having at least one inlet and at least one outlet, the inlet being structured to receive the extrusion mixture therethrough for passage into the barrel wherein a heat extraction structure cooperatively disposed with the barrel draws heat therefrom. An extrusion screw is disposed in the barrel and includes at least one screw flight structured to rotate within the barrel and urge the extrusion mixture towards the outlet of the barrel where a die is disposed in order to form the finished product. Moreover, the screw flight includes at least one circulation channel defined therein and structured to receive quantities of the extrusion mixture therethrough 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 prior to passage through the die.