Abstract: As has been established by ab-initio lattice QCD calculations, at T=156 MeV strongly interacting matter undergoes a crossover from the confined into a deconfined phase, called the Quark-Gluon Plasma (QGP). The properties of QGP are experimentally studied through heavy-ion collisions. From a theoretical point of view, an important question is how the onset of the formation of QGP during a heavy-ion collision can be identified. It had been argued in 1986 that formation of heavy quarkonia like J/ψ should be suppressed in the presence of QGP due to color screening. Since this suppression is reflected in the spectral functions of the quarkonia, we attempt to reconstruct these spectral functions from lattice correlators measured on new finite-temperature anisotropic ensembles, using the anisotropic Highly Improved Staggered Quark (aHISQ) action. We treat the valence heavy quarks that constitute the quarkonium with a lattice implementation of Nonrelativistic QCD (NRQCD).