A numerical nonisothermal two-phase wellbore model is developed to simulate downward flow of a steam and water mixture in the wellbore. This model entails simultaneous solution of coupled mass and momentum conservation equations inside the wellbore with an energy conservation equation for the fluids within the wellbore, surrounding medium and formation. A new drift-flux model that accounts for slip between the phases inside the wellbore is employed. In addition, a 2D implicit scheme that allows for heat transfer in both the axial and radial directions in the formation is developed. Furthermore, a rigorous nonlinear temperature- and depth-dependent overall heat transfer coefficient is implemented. The model predictions are validated against real field data and other available models. The model is useful for designing well completion and accurately computing the wellbore/formation heat transfer, which is important for estimating oil recovery by using steam injection.