  We calculate the in-medium masses of J/$\psi$ and of the excited states of
charmonium ($\psi$(3686) and $\psi$(3770)) in isospin asymmetric nuclear matter
at finite temperatures. These mass modifications arise due to the interaction
of the charmonium states with the gluon condensates of QCD, simulated by a
scalar dilaton field introduced to incorporate the broken scale invariance of
QCD within an effective chiral model. The change in the mass of J/$\psi$ in the
nuclear matter with density is seen to be rather small, as has been shown in
the literature by using various approaches, whereas, the masses of the excited
states of charmonium ($\psi$(3686) and $\psi$(3770)) are seen to have
considerable drop at high densities. The dependence of the masses of the
charmonium states on the isospin asymmetry has also been investigated in the
hot nuclear matter and is seen to be appreciable at moderate temperatures and
high densities. These medium modifications of the charmonium states should
modify the experimental observables arising from the compressed baryonic matter
produced in asymmetric heavy ion collision experiments in the future facility
of FAIR, GSI.
