A theoretical analysis is performed on unsteady thermal diffusion and fluid flow inside a cold open vessel resulting from warm liquid injection. A two-dimensional system is treated. The governing differential equations in dimension-less form are numerically solved by means of the finite difference techniques. In numerical computations, the aspect ratio of the open vessel as well as the location and flow rate are varied, while both the inlet warm liquid temperature and the final bulk temperature are specified. Results are obtained for the time history of the bulk liquid temperature and the timewise variations of the liquid velocity and temperature distribution throughout the entire vessel. It is disclosed that the introduction of a warm influx from a port on the left side wall yields a better mixing performance than from the base center of the vessel. This finding is in agreement with an existing experimental result.