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Several closely related ab initio thermal mean-field theories for fermions, both well-established and new ones, are compared with one another at the formalism level and numerically. The theories considered are Fermi-Dirac theory, thermal Hartree-Fock (HF) theory, two modifications of the thermal single-determinant approximation of Kaplan and Argyres, and first-order finite-temperature many-body perturbation theory based on zero-temperature or thermal HF reference. The thermal full-configuration-interaction theory is used as the benchmark.