  Recent lattice calculations showed that the quarkonia will survive beyond the
phase transition temperature, and will dissolve at different temperatures
depending on the type of the quarkonium. In this work, we calculate the thermal
width of the quarkonium at finite temperature before it dissolves into open
heavy quarks. The input of the calculation are the parton quarkonium
dissociation cross section to NLO in QCD, the quarkonium wave function in a
temperature-dependent potential from lattice QCD, and a thermal distribution of
partons with thermal masses. We find that for the J/psi, the total thermal
width above 1.4 Tc becomes larger than 100 to 250 MeV, depending on the
effective thermal masses of the quark and gluon, which we take between 400 to
600 MeV. Such a width corresponds to an effective dissociation cross section by
gluons between 1.5 to 3.5 mb and by quarks 1 to 2 mb at 1.4 Tc. However, at
similar temperatures, we find a much smaller thermal width and effective cross
section for the upsilon.
