  The $D$ and $\bar {D}$ mesons are studied in hot dense matter within a
self-consistent coupled-channel approach taking, as bare interaction, a broken
SU(4) s-wave Tomozawa-Weinberg interaction supplemented by an attractive
isoscalar-scalar term. The in-medium solution at finite temperature
incorporates Pauli blocking effects, baryon mean-field bindings, and $\pi$ and
open-charm meson self-energies. In the $DN$ sector, the $\Lambda_c$ and
$\Sigma_c$ resonances remain close to their free-space position while acquiring
a remarkable width. As a result, the $D$ meson spectral density shows a single
pronounced peak close to the free mass that broadens with increasing density
specially towards lower energies. The low-density theorem is not a good
approximation for the repulsive $\bar D$ self-energy close to saturation
density. We discuss the implications for the $J/\Psi$ suppression at CBM
(FAIR).
