Abstract: We study the temperature and baryon density dependence of the masses of the lightest charmed baryons Lambda(c), Sigma(c) and Sigma(c)*. We also look at the effects of the temperature and baryon density on the binding energies of the Lambda N-c and Lambda(c)Lambda(c) systems. Baryon masses and baryon-baryon interactions are evaluated within a chiral constituent quark model. Medium effects are incorporated in those parameters of the model related to the dynamical breaking of chiral symmetry, which are the masses of the constituent quarks, the sigma and pi meson masses, and quark-meson couplings. We find that while the in-medium Lambda(c) mass decreases monotonically with temperature, those of Sigma(c) and Sigma(c)* have a nonmonotonic dependence. These features can be understood in terms of a simple group theory analysis regarding the one-gluon exchange interaction in those hadrons. The in-medium Lambda N-c and Lambda(c)Lambda(c) interactions are governed by a delicate balance involving a stronger attraction due to the decrease of the sigma meson mass, suppression of coupled-channel effects and lower thresholds, leading to shallow bound states with binding energies of a few MeV. The Lambda(c) baryon could possibly be bound to a large nucleus, in qualitative agreement with results based on relativistic mean field models or QCD sum rules. Ongoing experiments at RHIC or LHCb or the planned ones at FAIR and J-PARC may take advantage of the present results.