A combined finite ele-ment/ streamline integration method is presented for nonisothermal flows of viscoelastic fluids. The attention is focused on some characteristic prob-lems that arise for numerical simula-tion of flows with high Deborah and Peclet numbers. The two most im-portant problems to handle are the choice of an outflow boundary con-dition for not completely developed flow and the treatment of the dissi-pative term in the temperature equa-tion. The ability of the numerical method to handle high Deborah and Peclet numbers will be demonstrated on a contraction flow of an LDPE melt with isotropic and anisotropic heat conductivity. The influence of anisotropic heat conduction and the difference between the stress work and mechanical dissipation will be discussed for contraction flows.