A collocated finite volume method on unstructured meshes is introduced to simulate the viscoelastic flow of the polymer melt with viscous dissipation past a confined cylinder. The constitutive equation for the simulations is non-isothermal FENE-P model, which is derived from the molecular theories. The temperature effect on the macroscopic fields (e.g., velocity, stress) and microscopic fields (e.g., molecular orientation, deformation, stretch) is investigated by comparison of isothermal and non-isothermal situations. This investigation indicates that temperature rise caused by viscous dissipation should not be neglected since it has significant effect on the macroscopic and microscopic properties of the polymer melt.