The present finite volume method based fluid flow solutions investigate the boundary-layer flow and heat transfer characteristics of polymer melt flow in a rectangular plane channel in the presence of the effect of viscous dissipation and heat transfer by considering the viscosity and density variations in the flow. For different inflow velocity boundary conditions and the injection polymer melt temperatures, the viscous dissipation effects on the velocity and temperature distributions are studied extensively to analyze the degree of interactions of thermal flow field dominated by the viscous heating and momentum diffusion mechanism with varying boundary conditions. The modified forms of Cross constitutive equation and Tait equation of state are adopted for the representation of viscosity variations and density change, respectively, in the polymer melt flow. These models together with the viscous dissipation terms are successfully incorporated into the finite volume method based fluid flow solutions to realistically represent the heat effects in the plane channel. The numerical results presented for two different commercial polymer melt flows, namely, polymer Polyacetal POM-M90-44 and polypropylene (PP), demonstrate that proposed mathematical formulations for viscosity and density variations including viscous heating terms into the energy equations, which are fully coupled with momentum equations, lead to more accurate representation of the fluid flow and heat transfer phenomena for the polymer melt flows in plane channels.