Numerical simulation for calculating temperature distributions, including the axial and radial temperature gradients in the melt spinning of polyethylene terephthalate (PET) monofilament, was performed. The finite difference method was used to calculate the radial temperature distribution. Newtonian and the upper convected Maxwell models were adopted as a constitutive equation, respectively. There is little difference in the axial and radial temperature profiles between Newtonian and the upper convected Maxwell constitutive equations. The effect of spinning conditions on the temperature difference between the core and surface was investigated. Quench air velocity is the most effective process variable in controlling the temperature difference. Quench air velocity profiles were investigated to reduce the temperature difference between the core and surface. Lower quench air velocity profile at initial deformation zone leads to a decrease in temperature difference between the core and surface. (c) 2006 Wiley Periodicals, Inc.