  The main objective of this work is to explore the evolution in the structure
of the quark-anti-quark bound states in going down in the chirally restored
phase from the so-called "zero binding points" $T_{zb}$ to the full
(unquenched) QCD critical temperature $T_c$ at which the Nambu-Goldstone and
Wigner-Weyl modes meet. In doing this, we adopt the idea recently introduced by
Shuryak and Zahed for charmed $\bar c c$, light-quark $\bar q q$ mesons $\pi,
\sigma, \rho, A_1$ and gluons that at $T_{zb}$, the quark-anti-quark scattering
length goes through $\infty$ at which conformal invariance is restored, thereby
transforming the matter into a near perfect fluid behaving hydrodynamically, as
found at RHIC. We show that the binding of these states is accomplished by the
combination of (i) the color Coulomb interaction, (ii) the relativistic
effects, and (iii) the interaction induced by the instanton-anti-instanton
molecules. The spin-spin forces turned out to be small. While near $T_{zb}$ all
mesons are large-size nonrelativistic objects bound by Coulomb attraction, near
$T_c$ they get much more tightly bound, with many-body collective interactions
becoming important and making the $\sigma$ and $\pi$ masses approach zero (in
the chiral limit). The wave function at the origin grows strongly with binding,
and the near-local four-Fermi interactions induced by the instanton molecules
play an increasingly more important role as the temperature moves downward
toward $T_c$.
