  We examine three different ways a heavy quarkonium can dissociate at high
temperatures. The heavy quarkonium can dissociate spontaneously when it becomes
unbound at a temperature above its dissociation temperature. Following the
recent work of Digal, Petreczky, and Satz, we calculate the dissociation
temperatures of heavy quarkonia taking into account the angular momentum
selection rules and using a temperature-dependent potential inferred from
lattice gauge calculations. We find that the selection rules change the
dissociation temperatures substantially for charmonia but only slightly for
bottomia. A quarkonium system in thermal equilibrium with the medium can
dissociate by thermalization. The fraction of quarkonium lying above the
dissociation threshold increases as temperature increases. A quarkonium can
also dissociate by colliding with light hadrons. We evaluate the cross sections
for the dissociation of $J/\psi$ and $\Upsilon$ in collision with $\pi$ as a
function of the temperature of the hadron medium, using the quark-interchange
model of Barnes and Swanson. We find that as the temperature increases, the
threshold energy decreases and the dissociation cross section increases.
