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

$D$ and $\bar{D}$ mesons in hot and dense matter