  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 $\Lambda_c N$ 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 $\Lambda_c N$ 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.
