This paper presents a three-dimensional transient finite element analysis code for solving the flow and heat transfer during polymer injection molding. The problems of interest present important challenges for both the physical modeling and the solution algorithm. The free surface flow of molten polymer moving inside the filling cavity has to be computed as well as the heat transfer between the polymer and the mold. During filling, heat transfer occurs at high Prandtl numbers because of the low material conductivity, resulting in sharp temperature gradients close to the walls. In this work the momentum, energy and front tracking equations are solved in a segregated manner. The energy equation is solved in an operator splitting approach. The methodology is robust and effective in solving three-dimensional industrial parts.