  The in-medium properties of charm mesons ($D$ and $\bar D$) in a hot and
dense matter are studied. A self-consistent coupled-channel approach is driven
by a broken SU(4) s-wave Tomozawa-Weinberg interaction supplemented by an
attractive isoscalar-scalar term. As medium effects, we include Pauli blocking,
baryon mean-field bindings, and $\pi$ and open-charm meson self-energies. The
dynamically generated $\tilde\Lambda_c$ and $\tilde\Sigma_c$ resonances in the
$DN$ sector remain close to their free space position but acquire large widths.
The resultant $D$ meson spectral function, which shows a single pronounced
quasiparticle peak close to the free mass that broadens with increasing
density, also has a long low energy tail associated with smeared
$\tilde\Lambda_c N^{-1}$, $\tilde\Sigma_c N^{-1}$ configurations. The
low-density approximation for the $\bar D N$ is questionable already at
subsaturation densities. We touch upon the implication of our study for
$J/\Psi$ suppression at FAIR.
