Comprehensive numerical computations are made of natural convection in a side-heated square cavity. Two layers of immiscible Boussinesq liquids are contained in the enclosure. Numerical solutions are acquired to the governing Navier-Stokes equations. No a priori assumptions are made on the shape and dynamical role of the interface. The behaviour of the interface is obtained as part of the solution. Attention is directed to the effect of a deformable interface and surface tension on the flow and heat transfer characteristics. Explicit influences of the capillary number and the Marangoni number are scrutinized. The global flow patterns are visualized, and local and averaged heat transfer coefficients along the wall are plotted. The limitations of the previous models using a non-deformable flat interface are pointed out.