A numerical model that incorporates temperature-dependent non-Newtonian viscosity was developed to simulate the extrusion process in extrusion-based additive manufacturing. Agreement with the experimental data was achieved by simulating a polylactic acid melt flow as a non-isothermal power law fluid using experimentally fitted parameters for polylactic acid. The model was used to investigate the temperature effect on the flow behavior, the cross-sectional area, and the uniformity of the extruded strand. OpenFOAM, an open source simulation tool based on the finite volume method, was used to perform the simulations. A computational module for solving the equations of non-isothermal multiphase flows was also developed to simulate the extrusion process under a small gap condition where the gap between the nozzle and the substrate surface is smaller than the nozzle diameter. Comparison of the strand shapes obtained from our model with isothermal Newtonian simulation, and experimental data confirms that our model improves the agreement with the experimental data. The result shows that the cross-sectional area of the extruded strand is sensitive to the temperature-dependent viscosity, especially in the small gap condition which has recently increased in popularity. Our numerical investigation was able to show nozzle temperature effects on the strand shape and surface topography which previously had been investigated and observed empirically only.