  We set up a framework in which in-medium charmonium properties are
constrained by thermal lattice QCD and subsequently implemented into a thermal
rate equation enabling the comparison with experimental data in heavy-ion
collisions. Specifically, we evaluate phenomenological consequences for
charmonium production originating from two different scenarios in which either
the free or the internal energy are identified with the in-medium 2-body
potential between charm and anti-charm quarks. These two scenarios represent
$J/\psi$ "melting temperatures" of approximately 1.25\,$T_c$ ("weak binding")
and 2\,$T_c$ ("strong binding"), respectively. Within current uncertainties in
dissociation rates and charm-quark momentum spectra, both scenarios can
reproduce the centrality dependence of inclusive $J/\psi$ yields in nuclear
collisions at SPS and RHIC reasonably well. However, the "strong-binding"
scenario associated the the internal energy as the potential tends to better
reproduce current data on transverse momentum spectra at both SPS and RHIC.
