  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.
