A kinetic-rate equation approach in a thermally expanding medium is employed to calculate the evolution of charmonium and bottomonium distributions in heavy-ion collisions. The equilibrium properties of the quarkonia are taken from in-medium spectral functions which are schematically constrained by euclidean correlators from lattice QCD. The initial conditions for the rate equation (heavy-flavor cross sections, nuclear absorption) and the thermal evolution are constrained by light-hadron data as available. After fixing two free parameters to describe charmonium data at SPS and RHIC, the predictions for LHC are discussed in light of recent data.