This paper provides accurate analytic models for a computationally efficient estimation of the natural con- vection cooling coefficients for typical geometries, such as those encountered in transformers. Proper thermal coordination is an essential step of any transformer design, especially when it comes to medium frequency operation, where the cooling surfaces are greatly reduced due to the frequency scaling. Available empirical formulas, derived for simple geometries, have a limited applicability to such complex structures. In this work, analytic models are derived based on extensive finite element method simulations that accurately describe the convective heat transfer of the geometries of interest. The proposed models improve accuracy substantially compared to the available models and have several orders of magnitude faster execution referred to finite element method simulations.