Employing the Phan-Thien tanner (PTT) fluids model, dynamic behavior of the non-isothermal melt spinning has been investigated. Subjects such as draw resonance instability, the effects of spinline cooling and of the fluid viscoelasticity on the spinning dynamics have been studied using the governing equations of the system. In particular, the draw resonance criterion based on the traveling times of various kinematic waves in the spinline has been confirmed, the reason why the spinline cooling is stabilizing is analyzed, and the effect of fluid viscoelasticity on the spinline stability is summarized. It is believed that the same method as in this study can be applied with equal ease to other extension deformation processes like film casting and film blowing.