Heat sinks in natural convection are thermally optimized by using the topology optimization method. To investigate the shape-dependent effect in natural convection, a new surrogate model accounting for the variation of the heat transfer coefficient within the computational domain is proposed. In order to validate the surrogate model, the result from topology optimization with the proposed surrogate model is compared to the plate-fin heat sink optimized using the existing correlation. From the comparison, it is found that the optimum channel spacing for the plate-fin heat sink is successfully reproduced by applying the surrogate model. With the validated surrogate model, a new conceptual design for a heat sink is obtained in the physical domain for which a conventional heat sink has been designed. To reflect the manufacturing constraints for mass production, guidelines for design simplification are suggested and applied to the conceptual design. Through the numerical simulation, it is found that the topology-optimized heat sink has 15% lower thermal resistance and 26% less material mass than the conventional heat sink.