  We calculate the mass shift and thermal decay width of the $J/\psi$ near the
QCD transition temperature $T_c$ by imposing two independent constraints on
these variables that can be obtained first by solving the Schr\"odinger
equation and second from the QCD sum rule approach. While the real part of the
potential is determined by comparing the QCD sum rule result for charmonium and
the D meson to that from the potential model result, the imaginary potential is
taken to be proportional to the perturbative form multiplied by a constant
factor, which in turn can be determined by applying the two independent
constraints. The result shows that the binding energy and the thermal width
becomes similar in magnitude at around $T=1.09T_c$, above which the sum rule
analysis also becomes unstable, strongly suggesting that the $J/\psi$ will melt
slightly above $T_c$.
