Using a combination of boundary element methods, finite element methods and streamline tracking for stresses, we explore the coupling between temperature‐induced swelling and stress‐induced swelling for materials with temperature‐dependent properties and a single relaxation time. One sees an interactive effect; the temperature‐ and stress‐induced swellings are not simply additive. The change of swelling shape is also noticeable. Calculations are reported for a temperature‐dependent Maxwell model up to a Weissenberg number of 1.5, and Weissenberg numbers up to 4.0 with the PTT model; Péclet numbers up to 200 are considered.