A two-dimensional conjugate heat transfer model has been developed for non-Newtonian materials being processed in a single screw extruder. Employing finite difference numerical methods, the governing equations for the fluid and solid regions are solved separately and an iterative numerical procedure is used for matching these solutions at the boundaries of the different regions, such as the barrel, screw and fluid domains, The flow and thermal fields in the screw channel for the non-Newtonian fluid and the thermal fields in the barrel and tie screw are obtained. It is found that heat conduction in the screw and in the barrel, particularly that in the latter, has a significant effect on the flow and on the thermal transport. The dependence of the process characteristics on the material properties, thermal boundary conditions, and on the dimensions of the extruder is determined, indicating the : need to consider conjugate transport effects for a realistic and accurate modeling of the process. These effects must also be included in the design and control of the extruder system in order to obtain optimal heat transfer and desired product quality.