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, Ann. Phys. 92, 1–24 (1975); and the first-order finite-temperature many-body perturbation theory based on a zero-temperature or thermal HF reference. Thermal full-configuration-interaction theory is used as the benchmark.