  We study the effect of a hot and dense medium on the binding energy of
hadronic molecules with open-charm mesons. We focus on a recent chiral
quark-model-based prediction of a molecular state in the $N \bar D$ system. We
analyze how the two-body thresholds and the hadron-hadron interactions are
modified when quark and meson masses and quark-meson couplings change in a
function of the temperature and baryon density according to predictions of the
Nambu--Jona-Lasinio model. We find that in some cases the molecular binding is
enhanced in medium as compared to their free-space binding. We discuss the
consequences of our findings for the search for exotic hadrons in high-energy
heavy-ion collisions as well as in the forthcoming facilities FAIR or J-PARC.
