A numerical approach is developed to study the thermal transport in polymer melts flowing through narrow channels with contraction. Attention is focused on the flow and heat transfer of practical polymer melts used in plastic industries, such as low-density polyethylene (LDPE), which cannot be regarded as Newtonian in their behavior. The rheological model used in this study is based on a power law variation of viscosity with shear rate, along with temperature and pressure dependent viscosity. The flow and heat transfer, which are strongly coupled through the temperature dependence of the viscosity, are solved by using a finite volume method with a nonuniform staggered grid system. The results are presented for axisymmetric tubes, which characterize the nozzle for an injection molding machine or the die in plastic extrusion. The effect of heat generation by viscous dissipation is included. The effects of varying the channel contraction ratio and other dimensions, as well as of the mass flow rate, are explored for channels with isothermal walls. The heat transfer rate, the pressure drop, and the temperature and shear stress distributions are determined. The results show that viscous dissipation significantly affects the temperature field and thus the heat transfer and shear stress in the narrowing region. The maximum temperature is observed near but not at the wall of the constricted portion of the channel. The influence of pressure on viscosity is usually neglected for low-pressure situations. However, this effect is not negligible when the magnitude of pressure is very large, as is the case for many practical problems, and is included in the investigation.