  We study quarkonium correlators and spectral functions at zero and finite
temperature in QCD with only heavy quarks using potential models combined with
perturbative QCD. First, we show that this approach can describe the quarkonium
correlation function at zero temperature. Using a class of screened potentials
based on lattice calculations of the static quark-antiquark free energy we
calculate spectral functions at finite temperature. We find that all quarkonium
states, with the exception of the $1S$ bottomonium, dissolve in the deconfined
phase at temperatures smaller than $1.5T_c$, in contradiction with the
conclusions of recent studies. Despite this the temperature dependence of the
quarkonium correlation functions calculated on the lattice is well reproduced
in our model. We also find that even in the absence of resonances the spectral
function at high temperatures is significantly enhanced over the spectral
function corresponding to free quark antiquark propagation.
