The purpose of this study is to develop a steady-state thermal model for melt spinning of polyester fiber by incorporating the radial heat conduction inside the fiber and the combined effect of radiation and convection at the boundary. The governing equations are obtained from the energy, mass, and momentum balances coupling with the rheological properties of the fibers. The effects of drag, surface tension, gravity, and inertia force are also taken into consideration in the analysis. The velocity profile, temperature profile, and the variation of cross-sectional area of the filament along the axial direction are solved by employing a finite-difference scheme.