  Charmonium spectral functions in vector and pseudoscalar channels at finite
temperature are investigated through the complex Borel sum rules and the
maximum entropy method. Our approach enables us to extract the peaks
corresponding to the excited charmonia, $\psi^\prime$ and $\eta_c^\prime$, as
well as those of the ground states, $J/\psi$ and $\eta_c$, which has never been
achieved in usual QCD sum rule analyses. We show the spectral functions in
vacuum and their thermal modification around the critical temperature, which
leads to the almost simultaneous melting (or peak disappearance) of the ground
and excited states.
