  The thermal evolution of the spectral densities derivable from the two-point
functions of the elementary and the quadratic composite fields of the O(N)
model is studied in the isosinglet channel and in the broken symmetry phase at
infinite N. The results are applied with realistic parameter values to the N=4
case. They provide a reasonable description of the $\sigma$ meson at T=0.
Threshold enhancement is observed around $T\sim 1.07m_\pi$. For higher
temperatures the maximum of the spectral function in the single meson channel
decreases and becomes increasingly rounded.
