  We evaluate the in-medium $D$ and $\bar D$-meson masses in hot hadronic
matter induced by interactions with the light hadron sector described in a
chiral SU(3) model. The effective Lagrangian approach is generalized to SU(4)
to include charmed mesons. We find that the D-mass drops substantially at
finite temperatures and densities, which open the channels of the decay of the
charmonium states ($\Psi^\prime$, $\chi_c$, $J/\Psi$) to $D \bar D$ pairs in
the thermal medium. The effects of vacuum polarisations from the baryon sector
on the medium modification of the $D$-meson mass relative to those obtained in
the mean field approximation are investigated. The results of the present work
are compared to calculations based on the QCD sum-rule approach, the
quark-meson coupling model, chiral perturbation theory, as well as to studies
of quarkonium dissociation using heavy quark potential from lattice QCD.
