  We study charmonium correlators in pseudoscalar and vector channels at finite
temperature using lattice QCD simulation in the quenched approximation.
Anisotropic lattices are used in order to have sufficient numbers of degrees of
freedom in the Euclidean temporal direction. We focus on the low energy
structure of the spectral function, corresponding to the ground state in the
hadron phase, by applying the smearing technique to enhance the contribution to
the correlator from this region. We employ two analysis procedures: the maximum
entropy method (MEM) for the extraction of the spectral function without
assuming a specific form, to estimate the shape of the spectral function, and
the standard $\chi^2$ fit analysis using typical forms in accordance with the
result of MEM, for a more quantitative evaluation. To verify the applicability
of the procedures, we first analyze the smeared correlators as well as the
point correlators at zero temperature. We find that by shortening the
$t$-interval used for the analysis (a situation inevitable at $T>0$) the
reliability of MEM for point correlators is lost, while it subsists for smeared
correlators. Then the smeared correlators at $T\simeq 0.9 T_c$ and $1.1 T_c$
are analyzed. At $T\simeq 0.9 T_c$, the spectral function exhibits a strong
peak, well approximated by a delta function corresponding to the ground state
with almost the same mass as at T=0. At $T\simeq 1.1 T_c$, we find that the
strong peak structure still persists at almost the same place as below $T_c$,
but with a finite width of a few hundred MeV. This result indicates that the
correlators possess a nontrivial structure even in the deconfined phase.
