Transient two-dimensional laminar convective cooling of water in an enclosed rectangular cavity with a convective boundary condition is approached by a numerical method. The maximum density effect and supercooling are considered in order to understand the flow and temperature fields in a mass of water cooled to a temperature near its freezing point. The time dependent flow and temperature fields, mixed mean, center point, maximum wall temperature and the heat transfer rate on each wall are presented. The computations are performed mainly for the case of a square cavity but the influence of the aspect ratio of the cavity is also discussed.