  We calculate the $\phi$-meson propagator at finite temperature at the
one--loop order. The real and imaginary parts are studied separately in full
kinematic ranges. From this activity we investigate how temperature affects
such things as decay widths and dispersion relations. {}From here we estimate
the thermal rate of lepton pair radiation in a hadron gas proceeding through
$K^{+}K^{-}\to \phi \to \ell^{+}\ell^{-}$ and $\pi\rho\to \phi \to
\ell^{+}\ell^{-}$. We find several interesting things. From the dispersion
relations we learn the effective mass calculated this way increases with
temperature as does the partial width, but only slightly. At $T=200$ MeV, the
mass increases by $\sim$ 4 MeV and the partial width increases by 34\%.
Polarizations are indistinguishable for practical purposes.
