  The thermal evolution of the hadronic parameters of charmonium in the vector
channel, i.e. the J/psi resonance mass, coupling (leptonic decay constant),
total width, and continuum threshold is analyzed in the framework of thermal
Hilbert moment QCD sum rules. The continuum threshold $s_0$, as in other
hadronic channels, decreases with increasing temperature until the PQCD
threshold s_0 = 4, m_Q^2 is reached at T \simeq 1.22T_c (m_Q is the charm quark
mass) and the J/psi mass is essentially constant in a wide range of
temperatures. The other hadronic parameters behave in a very different way from
those of light-light and heavy-light quark systems. The total width grows with
temperature up to T \simeq 1.04T_c beyond which it decreases sharply with
increasing T. The resonance coupling is also initially constant beginning to
increase monotonically around T \simeq T_c. This behavior strongly suggests
that the J/psi resonance might survive beyond the critical temperature for
deconfinement, in agreement with lattice QCD results.
