A nonisothermal model of Ike single screw extrusion processing of generalized Newtonian fluids is presented. Various temperature dependent forms of a generalized Newtonian fluid constitutive equation representing the Herschel-Bulkley fluid and its simplifications, including Bingham plastic, power law of Ostwald-de Waele, and Newtonian fluids, are applicable. The model includes the generally ignored transverse convection terms of the equation of energy. The importance of keeping the transverse convection terms in the analysis is demonstrated by applying the model and comparing findings to experimental results involving the transverse flow temperature distributions in single screw extruders, available in the literature. The numerical instabilities, arising principally from the convection terms, generally encountered in high-Péclet-number extrusion flows, could be eliminated by the use of the streamline upwind / Petrov-Galerkin formulation. The model is sufficiently general to accommodate Navier's wall slip at the wall boundary condition commonly encountered during the processing of gels and concentrated suspensions.