  Thermal density functional theory calculations often use the Mermin-Kohn-Sham
scheme, but employ ground-state approximations to the exchange-correlation (XC)
free energy. In the simplest solvable nontrivial model, an asymmetric Hubbard
dimer, we calculate the exact many-body energies and the exact Mermin-Kohn-Sham
functionals for this system and extract the exact XC free energy. For moderate
temperatures and weak correlation, we find this approximation to be excellent.
We extract various exact free-energy correlation components and the exact
adiabatic connection formula.
