  We study how we can understand the change of the spectral function and the
pole location of the correlation function for sigma at finite temperature,
which were previously obtained in the linear sigma model with a resummation
technique called optimized perturbation theory. There are two relevant poles in
the sigma channel. One pole is the original sigma pole which shows up as a
broad peak at zero temperature and becomes lighter as the temperature
increases. The behavior is understood from the decreasing of the sigma
condensate, which is consistent with the Brown-Rho scaling. The other pole
changes from a virtual state to a bound state of pion-pion as the temperature
increases which causes the enhancement at the pion-pion threshold. The behavior
is understood as the emergence of the pion-pion bound state due to the
enhancement of the pion-pion attraction by the induced emission in medium. The
latter pole, not the former, eventually degenerates with pion above the
critical temperature of the chiral transition. This means that the observable
"sigma" changes from the former to the latter pole, which can be interpreted as
the level crossing of "sigma" and pion-pion at finite temperature.
