Draw resonance is caused by a constant speed winder that leads to non-constant axial forces (Schultz, 1984). The well studied isothermal Newtonian fiber drawing predicts very modest critical draw ratios (around 20, much less than the typical production draw ratios for glass fibers of 10(3) - 10(5)). The nonisothermal fiber drawing model presented here shows that cooling along the spin line strongly stabilizes the process. However, we show that the conclusion of Shah and Pearson (1972a,b) that nonisothermal Newtonian fiber spinning is unconditionally stable is based on non-converged numerical results. The choice of viscosity-temperature correlation function has a strong influence in determining the stability of the process. While viscoelasticity generally has an adverse effect on the stability, low viscoelasticity in the presence of extensional thinning helps to slightly improve the maximum critical draw ratio.