  We calculate in a general background gauge, to one-loop order, the leading
logarithmic contribution from the graviton self-energy at finite temperature
$T$, extending a previous analysis done at $T=0$. The result, which has a
transverse structure, is applied to evaluate the leading quantum correction of
the gravitational vacuum polarization to the Newtonian potential. An analytic
expression valid at all temperatures is obtained, which generalizes the result
obtained earlier at $T=0$. One finds that the magnitude of this quantum
correction decreases as the temperature rises.
