Non-isothermal extrudate swell problems for viscoelastic fluids have been solved by employing a modified non-consistent streamline upwind mixed finite element method with the White-Metzner constitutive equation. The computation was shown to be stable and to converge up to extrusion rates significantly higher than those used in previous studies which employed conventional finite element methods. Additionally, the effects of viscous dissipation at high extrusion rates and various cooling rates have been discussed. Furthermore, the effects of two kinds of artificial diffusivities and various forms of material functions on the swell ratio and the free surface profiles have been discussed. The extrudate swell has been shown to exhibit an important temperature dependence.