  We calculate the adiabatic contributions to the free energy due to the
electron--phonon interaction at intermediate temperatures, $0 \leqslant k_{B} T
< \epsilon_{F}$ for the elemental metals Na, K, Al, and Pb. Using our
previously published results for the nonadiabatic contributions we show that
the adiabatic contribution, which is proportional to $T^{2}$ at low
temperatures and goes as $T^{3}$ at high temperatures, dominates the
nonadiabatic contribution for temperatures above a cross--over temperature,
$T_{c}$, which is between 0.5 and 0.8 $T_{m}$, where $T_{m}$ is the melting
temperature of the metal. The nonadiabatic contribution falls as $T^{-1}$ for
temperatures roughly above the average phonon frequency.
