  We obtain the D-meson spectral density at finite temperature for the
conditions of density and temperature expected at FAIR. We perform a
self-consistent coupled-channel calculation taking, as a bare interaction, a
separable potential model. The $\Lambda_c$ (2593) resonance is generated
dynamically. We observe that the D-meson spectral density develops a sizeable
width while the quasiparticle peak stays close to the free position. The
consequences for the D-meson production at FAIR are discussed.
