  We study the effect of thermal width of $\pi$ on the spectral function of
$\sigma$ applying a resummation technique called optimized perturbation theory
at finite temperature ($T$) to ${\cal O}(4)$ linear sigma model. In order to
take into account finite thermal width of $\pi$, we replace the internal pion
mass in the self-energy of $\sigma$ with that of complex pole found in a
previous paper. The obtained spectral function for $T\aplg 100 {\rm MeV}$ turns
out to possess two broad peaks. Although a sharp peak at $\sigma\to\pi\pi$
threshold was observed in the one-loop calculation without pion thermal width,
the peak is proved to be smeared out. We also search for the poles of the
$\sigma$ propagator and analyze the behavior of the spectral function with
these poles.
