A design approach is proposed and demonstrated to identify desirable two-dimensional solid geometries, cooled by natural convection, that offer superior thermal performance in terms of reduced overall (conduction-convection) thermal resistance. The approach utilizes (i) heat transfer modeling in conjunction with (ii) various novel shape evolution rules. Predictions demonstrate the evolution of the solid shape and associated reduction of the overall thermal resistance. Parametric simulations reveal the dependence of the predicted solid shape on the evolution rule employed, the thermal conductivity of the solid material, and the strength of advection within the fluid.