The inception of adiabatic steady shear Bow of a dilute polymer solution modeled as Hookean dumbbells is considered. The effects of temperature variations in the flow are included explicitly in the constitutive equation. These temperature variations are caused in the Bow by the conversion of mechanical energy (work) into thermal energy through the process known as viscous dissipation. However, in a polymeric liquid, part of the mechanical work is also stored by the material as elastic energy, and we account for this energy by including the nonequilibrium nature of the internal energy function. The model predicts significant temperature increases in the material upon the inception of shear flow. Stress overshoots and long-time decay are also predicted in contrast to the monotonic stress growth predicted for the isothermal system.