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We propose a combined ab initio-spin quantum Monte Carlo (QMC) approach to compute thermodynamic properties of magnetic materials by first principles. The key to the proposed approach is a mapping of the magnetic long-range system onto an effective, nearest-neighbor quantum Heisenberg model, for which the QMC approach provides a numerically exact solution. The performance of the proposed method is demonstrated for the transition metals Fe, Co, and Ni by computing magnetization shapes, specific heat capacities, and free energies. Spin-quantization effects are found to be critical, even close to T-C.