Abstract: This paper presents the results of meshless or mesh free analysis of a heat transfer problem of polymer melt flowing in a tube at constant ambient temperature.Here, the rheological behavior of the melt was described by a temperature dependent power-law model with viscous dissipation.Temperature profiles were obtained for different tube lengths.Comparing with the no viscous dissipation model, it was shown that the temperature-dependent viscous dissipation term had significant impact on the heat transfer，i.e., the temperature difference between the model with temperature-dependent power-law viscous dissipation and the model without viscous dissipation was about 64℃.Moreover, the limiting temperature profiles of both no viscosity dissipation model and temperature-dependent power-law model were influenced by the wall boundary, but not by the inlet conditions of the polymer melt.