The time‐dependent nonisothermal elongational flows of polymeric fluids have been modeled using the Leonov constitutive theory. The stress growth at a constant elongational strain rate or constant pulling speed and stress relaxation after elongation have been considered under various thermal histories including constant cooling rate and a sudden jump or a drop in temperature. Following the concept of thermorheological simplicity, the nonisothermal effects have been conveniently incorporated into the theory via experimentally determined temperature shift factors together with the effect of nonzero cooling rates on glass transition temperature. The predicted results have been compared with the available experimental data of Bogue and co‐workers. In general, the agreement between theory and experiment is found to be good and comparable to the available results of other theories.