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Motivated by the recent lattice data that $J/\psi$ will survive up to1.6$T_c$, we calculate the thermal width of $J/\psi$ at finite temperature inperturbative QCD. The inputs of the calculation are the parton quarkoniumdissociation cross sections at the NLO in QCD, which were previously obtainedby Song and Lee, and a gaussian charmonium wave function, whose size werefitted to an estimate by Wong by solving the schrodinger equation forcharmonium in a potential extracted from the lattice at finite temperature. Wefind that the total thermal width above 1.4$T_c$ becomes larger than 100 to 200MeV, depending on the effective thermal masses of the quark and gluon, which wetake it to vary from 600 to 400 MeV.Comment: 4 pages, Talk at Quark Matter 200

J/ψ hadron interaction in vacuum and in QGP