  We investigate the properties of heavy quarkonia at finite temperature in
detail using QCD sum rules. Extending previous analyses, we take into account a
temperature dependent effective continuum threshold and derive constraints on
the mass, the width, and the varying effective continuum threshold. We find
that at least one of these quantities of a charmonium changes abruptly in the
vicinity of the phase transition. We also calculate the ratio of the imaginary
time correlator to its reconstructed one, $G/G_{\text{rec}}$, by constructing a
model spectral function and compare it to the corresponding lattice QCD
results. We demonstrate that the almost constant unity of $G/G_{\text{rec}}$
can be obtained from the destructive interplay of the changes in each part of
the spectral modification which are extracted from QCD sum rules.
