  Motivated by the recent lattice data that $J/\psi$ will survive up to
1.6$T_c$, we calculate the thermal width of $J/\psi$ at finite temperature in
perturbative QCD. The inputs of the calculation are the parton quarkonium
dissociation cross sections at the NLO in QCD, which were previously obtained
by Song and Lee, and a gaussian charmonium wave function, whose size were
fitted to an estimate by Wong by solving the schrodinger equation for
charmonium in a potential extracted from the lattice at finite temperature. We
find that the total thermal width above 1.4$T_c$ becomes larger than 100 to 200
MeV, depending on the effective thermal masses of the quark and gluon, which we
take it to vary from 600 to 400 MeV.
