To demonstrate the influence of molecular orientation on the heat conduction in a flowing polymeric liquid, we consider a variant of the Graetz-Nusselt problem. A polymeric liquid is flowing between two flat, parallel plates with a sudden change in the wall temperature. The temperature distribution in the entrance region is calculated numerically taking viscous dissipation into account. It is assumed that the material properties are independent of the temperature. It is shown that the change in the temperature distribution in the fluid caused by molecular orientation is large enough to affect polymer processing significantly.