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The thermodynamic properties of cementite have been evaluated with a hybrid approach, which describes the vibrational and electronic excitations based on density functional theory calculations, while the magnetic free energy is evaluated using the spin quantum Monte Carlo scheme. Our ansatz allows us to calculate the heat capacity and free energy of cementite with a high accuracy resulting in a free-energy difference of less than 10 meV/atom at 1500 K when compared with experiment. For the formation energy of cementite we observe, however, that the accuracy of density functional theory within the Perdew-Burke-Ernzerhof exchange-correlation functional is not sufficient to provide quantitative agreement with experiment. We show that the main limit in the accuracy of this exchange-correlation functional is the T=0 K potential energy surface.