Currently used methods for the description of thermodynamics of ferroelectric thin films (Landau theory or ab initio based Monte Carlo simulations) are based on an energy expansion in terms of internal degrees of freedom. It was shown that these methods can suffer from a substantial inaccuracy unless higher order electromechanical interactions are taken into account. The high-order electromechanical couplings strongly renormalize the sixth-power polarization terms of the thermodynamic energy expansion. In this paper, apart from the general statement, we illustrate it with an example of a temperature-misfit strain phase diagram of a BaTiO3 thin film derived with high-order electromechanical interactions evaluated using first-principles calculations.