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A combined ab initio approach to calculate the thermodynamic properties of bcc iron including vibrational, electronic, and magnetic free-energy contributions is derived. Special emphasis is placed on the magnetic contribution that is obtained using the frozen-magnon approach combined with Monte Carlo (MC) calculations. The importance of spin quantum-mechanical effects has been studied for magnetically nonfrustrated model systems by comparing classical and quantum MC. Based on this analysis, we propose a rescaling scheme which allows an approximate ad hoc inclusion of the quantum effects into the classical MC simulations. The rescaled MC scheme is found to be robust with respect to the specific magnetic configuration and the lattice type and is therefore expected to yield an approximate yet reliable description of the magnetic contribution for cases where quantum MC calculations are not practical. Applying the method to bcc iron and combining the magnetic, vibronic and electronic contributions, we find an excellent agreement with experimental data for the heat capacity and free energy, both, below and above the Curie temperature.