Abstract: In this paper, the streamline upwind Petrov - Galerkin (SUPG) F E M and Galerkin F E M are used to simulate the non - isothermal flow of the Carreau fluid in an agitated vessel induced by scraped -surface blades. The results show a great deviation from the isothermal Newtonian flow, and indicate that the power - law exponent n, temperature coefficient b, dimensionless groups Re, Pe, and Br have a distinct effect on the flow pattern. This work provides an effective numerical method for predicting the velocity profile, temperature, shear rate and shear stress distribution of non - isothermal, non - Newtonian -flow in an agitated vessel.