  The thermal properties of the glueballs are studied using SU(3) anisotropic
lattice QCD with beta=6.25, the renormalized anisotropy xi=a_s/a_t=4 over the
lattice of the size 20^3\times N_t with N_t = 24, 26, 28, 30, 33, 34, 35, 36,
37, 38, 40, 43, 45, 50, 72 at the quenched level. To construct a suitable
operator on the lattice, we adopt the smearing method, and consider its
physical meaning in terms of the operator size. First, we construct the
temporal correlators G(t) for the 0^{++} and 2^{++} glueballs, using more than
5,000 gauge configurations at each temperature. We then measure the pole-mass
of the thermal glueballs from G(t). For the lowest 0^{++} glueball, we observe
a significant pole-mass reduction of about 300 MeV near T_c or m_G(T\simeq T_c)
\simeq 0.8 m_G(T\sim 0), while its size remains almost unchanged as rho(T)
\simeq 0.4fm. Finally, for completeness, as an attempt to take into account the
effect of thermal width Gamma(T) at finite temperature, we perform a more
general new analysis of G(t) based on its spectral representation. By adopting
the Breit-Wigner form for the spectral function rho(omega), we perform the
best-fit analysis as a straightforward extension to the standard pole-mass
analysis. The result indicates a significant broadening of the peak as Gamma(T)
\sim 300 MeV as well as rather modest reduction of the peak center of about 100
MeV near T_c for the lowest 0^{++} glueball. The temporal correlators of the
color-singlet modes corresponding to these glueballs above T_c are also
investigated.
