Numerical predictions of the three-dimensional temperature and velocity profiles of an experimental stratified horizontal pipe flow are performed. The experiment is one of a series of flow tests conducted at Argonne National Laboratory. A new accurate and stable skew-upwind differencing scheme is employed in the finite difference solution of the energy equation. The skew-upwind predictions are in excellent agreement with the experimental data as steady-state conditions are approached at the upstream test subsection. Comparisons between the conventional upwind and the skew-upwind schemes showed that the skew-upwind formulation provided a significant increase in the accuracy of temperature predictions.