An iterative stabilized fractional step scheme abbreviated as I-CNBS-CG is developed, in which the Crank-Nicolson method based split (CNBS) scheme and the characteristic-Galerkin (CG) method are, respectively, used to discretize and solve the non-Newtonian momentum-mass conservation equations and the energy conservation equation in consideration of their convective character. Owing to introduction of an iterative procedure into the scheme the stability of the proposed scheme in time domain is greatly enhanced and much larger time step sizes are allowed to be used than those limited in existing explicit and semi-implicit ones. The proposed I-CNBS-CG scheme particularly suits to numerically model the non-isothermal non-Newtonian fluid flows with moderate or high viscosity and low thermal conductivity, such as molten polymer flow process in a mould cavity. Numerical experiments with the power-law fluid model demonstrate the improved performances of the proposed scheme. (c) 2006 Elsevier Ltd. All rights reserved.