During the molding of industrial parts using injection molding, the molten polymer flows through converging and diverging sections as well as in areas presenting thickness and flow direction changes. A good understanding of the flow behavior and thermal history is important in order to optimize the part design and molding conditions. This is particularly true in the case of automotive and electronic applications where the coupled phenomena of fluid flow and heat transfer determine to a large extent the final properties of the part. This paper presents a 3D finite element model capable of predicting the velocity, pressure, and temperature fields, as well as the position of the flow fronts. The velocity and pressure fields are governed by the generalized Stokes equations. The fluid behavior is predicted through the Carreau Law and Arrhenius constitutive models. These equations are solved using a Galerkin formulation. A mixed formulation is used to satisfy the continuity equation. The tracking of the flow front is modeled by using a pseudo-concentration method and the model equations are solved using a Petrov-Galerkin formulation. The validity of the method has been tested through the analysis of the flow in simple geometries. Its practical relevance has been proven through the analysis of an industrial part.