One of the common processes to draw molten polymer jets into micron and submicron scale fibers is melt electrospinning, where an electric field is used to elongate and accelerate charged materials. However, modeling for melt electrospinning was commonly done at continuum level and cannot predict the instability of jet motion. In this study, discretized models, which were reported to have an excellent prediction on the jet motion including the instability in solution-based electrospinning, for electrically driven molten polymer jet was developed. Discretized models are based on describing the fluid jet as a series of beads connected by viscoelastic spring, followed by solving the force balance on each bead, allowing the facile probing of the unstable downstream jet. This study focused on developing a discretized model to employ non-isothermal aspects on the stable polymer melt jet for melt electrospinning. The simulation results were compared with simulation results shown in literature to verify that model’s predictions are comparable.