A numerical study of nonisothermal viscoelastic flow is conducted to investigate the complex flow characteristics of polymer melts in the extrusion process. A general thermodynamic model for the energy conversion related to viscoelastic fluid flow is introduced. The mathematical model for three-dimensional nonisothermal viscoelastic flow of the polymer melts obeying a differential constitutive equation (Phan-Thien and Tanner model) is established. A decoupled algorithm based on the penalty finite element method is performed on the calculation. The discrete elastic-viscous split stress (DEVSS) algorithm, incorporating the streamline-upwind Petrov-Galerkin (SUPG) scheme is employed to improve the computation stability. Essential flow characteristics of polymer melts in the extrusion die for hollow square plastic profile is investigated based on the proposed numerical scheme with ignoring the outer thermal resource. The energy partitioning, which quantified the conversion of mechanical energy into thermal energy, is discussed. The effects of volume flow rate and die contraction angle upon the flow patterns are further investigated. POLYM. ENG. SCI., 48:316-328, 2008. (c) 2007 Society of Plastics Engineers.