  First we summarize the quark-level linear $\sigma$ model compositeness
conditions and verify that indeed $m_\sigma = 2 m_q$ when $m_\pi = 0$ and
$N_c=3$, rather than in the $N_c\to\infty$ limit, as is sometimes suggested.
Later we show that this compositeness picture also predicts a chiral symmetry
restoration temperature $T_c = 2f_\pi$, where $f_\pi$ is the pion decay
constant. We contrast this self-consistent Z=0 compositeness analysis with
prior studies of the compositeness problem.
