  Starting from an earlier representation of the independent dimension 6 gluon
operators in terms of color electric and magnetic fields, we estimate their
changes near the critical temperature $T_c$ using the temperature dependence of
the dimension 4 electric and magnetic condensates extracted from pure gauge
theory on the lattice. We then improve the previous QCD sum rules for the
$J/\psi$ mass near $T_c$ based on dimension 4 operators, by including the
contribution of the dimension 6 operators to the OPE. We find an enhanced
stability in the sum rule and confirm that the $J/\psi$ will undergo an abrupt
change in the property across $T_c$.
