  Using the potential model and thermodynamical quantities obtained in lattice
gauge calculations, we determine the spontaneous dissociation temperatures of
color-singlet quarkonia and the `quark drip lines' which separate the region of
bound $Q\bar Q$ states from the unbound region. The dissociation temperatures
of $J/\psi$ and $\chi_b$ in quenched QCD are found to be 1.62$T_c$ and
$1.18T_c$ respectively, in good agreement with spectral function analyses. The
dissociation temperature of $J/\psi$ in full QCD with 2 flavors is found to be
1.42$T_c$. For possible bound quarkonium states with light quarks, the
characteristics of the quark drip lines severely limit the stable region close
to the phase transition temperature. Bound color-singlet quarkonia with light
quarks may exist very near the phase transition temperature if their effective
quark mass is of the order of 300-400 MeV and higher.
