The quantum-mechanical partition function for a system of interacting electrons and nuclei is examined in the "classical" limit, in which $\ensuremath{\hbar}\ensuremath{\rightarrow}0$ in the nuclear kinetic energy operator while $\ensuremath{\hbar}$ is constant in the electronic kinetic energy operator. It is shown that in the "classical" limit, the apparent nuclear potential energy which appears in the partition function is actually the free energy of the electrons in a system of fixed nuclei, as a function of nuclear configuration and temperature. The lowest order quantum correction is obtained. The effect of the adiabatic approximation is studied; it leads to the correct "classical" limit but a formally inexact lowest order quantum correction.