  We study the properties of $D$ and $\bar{D}$ mesons in hot isospin asymmetric
strange hadronic matter, arising due to their interactions with the hadrons in
the hyperonic medium. The interactions of $D$ and $\bar{D}$ mesons with these
light hadrons are derived by generalizing the chiral SU(3) model used for the
study of hyperonic matter to SU(4). We also study the mass modifications of the
charmonium states $J/\psi$, $\psi(3686)$ and $\psi(3770)$ in the isospin
asymmetric strange hadronic matter at finite temperatures and investigate the
possibility of the decay of the charmonium states into $D\bar D$ pairs in the
hot hadronic medium. The mass modifications of these charmonium states arise
due to their interaction with the gluon condensates of QCD, simulated by a
scalar dilaton field introduced to incorporate the broken scale invariance of
QCD within the effective chiral model. We also compute the partial decay widths
of the charmonium states to the $D\bar {D}$ pairs in the hadronic medium. The
strong dependence on density of the in-medium properties of the $D$, $\bar{D}$
and the charmonium states, as well as the partial decay widths of charmonium
states to $D\bar {D}$ pairs, found in the present investigation, will be of
direct relevance in observables like open charm enhancement as well as $J/\psi$
suppression in the compressed baryonic matter (CBM) experiments at the future
Facility for Antiproton and Ion Research, GSI, where the baryonic matter at
high densities is planned to be produced.
