  We study the in-medium properties of $D$ and $\bar{D}$ mesons in
isospin-asymmetric nuclear matter at finite temperatures using an effective
chiral SU(4) model. The interactions of $D$ and $\bar{D}$ mesons with nucleons,
scalar isoscalar meson $\sigma$, and scalar iso-vector meson $\delta$ are taken
into consideration. It is found that as compared to the $\bar{D}$ mesons, the
properties of the $D$ mesons are observed to be quite sensitive to the
isospin-asymmetry at high densities. At finite densities, the masses of $D$ and
$\bar{D}$ mesons observed at finite temperatures are seen to be higher in
comparison to the zero temperature case. The present study of the in-medium
properties of $D$ and $\bar{D}$ mesons will be of relevance for the experiments
in the future facility of the FAIR, GSI, where the compressed baryonic matter
at high densities and moderate temperatures is expected to be produced. The
mass modifications of $D$ and $\bar{D}$ mesons in hot nuclear medium can lead
to decay of the charmonium states ($\Psi^{'}, \chi_{c}, J/\Psi$) to $D\bar{D}$
pairs in dense hadronic matter. The isospin-asymmetric effects on the
properties of the open charm mesons for the doublets $D=(D^0,D^+)$ and $\bar
D=(\bar D^0,D^-)$ should show in observables like their production and
collective flow in asymmetric heavy-ion collisions. The small attractive
potentials observed for the $\bar{D}$ mesons may also lead to formation of the
$\bar{D}$ mesic nuclei.
