  We study the one-loop contributions of matter and radiation to the
gravitational polarization tensor at finite temperatures. Using the
analytically continued imaginary-time formalism, the contribution of matter is
explicitly given to next-to-leading ($T^2$) order. We obtain an exact form for
the contribution of radiation fields, expressed in terms of generalized Riemann
zeta functions. A general expression is derived for the physical polarization
tensor, which is independent of the parametrization of graviton fields. We
investigate the effective thermal masses associated with the normal modes of
the corresponding graviton self-energy.
