Three-dimensional numerical computations of negatively buoyant cold jet injected into hot water flowing in a pipe are presented for various hot-to-cold flow rate ratios. A fine nodalization with a newly modified skew upwind differencing scheme is employed. The adoption of this scheme results in a significant reduction of the numerical diffusion errors. Under certain conditions of the jet Froude number, the hot water penetrates upward into the injector, resulting in a recirculatory flow region. Such penetration and recirculation enhance the mixing process, thus helping mitigate the pressurized thermal shock concern. A satisfactory agreement between the numerical temperature predictions with available experimental data is obtained.