We investigate charmonium production in the hot medium created by heavy-ion collisions by setting up a framework in which in-medium charmonium properties are constrained by thermal lattice QCD (lQCD) and subsequently implemented into kinetic approaches. A Boltzmann transport equation is employed to describe the time evolution of the charmonium phase space distribution with the loss and gain term accounting for charmonium dissociation and regeneration (from charm quarks), respectively. The momentum dependence of the charmonium dissociation rate is worked out. The dominant process for in-medium charmonium regeneration is found to be a 3-to-2 process. Its corresponding regeneration rates from different input charm-quark momentum spectra are evaluated. Experimental data on $J/psi$ production at CERN-SPS and BNL-RHIC are compared with our numerical results in terms of both rapidity-dependent inclusive yields and transverse momentum ($p_t$) spectra. Within current uncertainties from (interpreting) lQCD data and from input charm-quark spectra the centrality dependence of $J/psi$ production at SPS and RHIC (for both mid- and forward rapidity) is reasonably well reproduced. The $J/psi$ $p_t$ data are shown to have a discriminating power for in-medium charmonium properties as inferred from different interpretations of lQCD results.
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