  The main objective of this work is to explore the evolution in the structure
of the quark-antiquark bound states in going down in the chirally restored
phase from the so-called "zero binding points" T_zb to the 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-antiquark scattering length goes through
infinity 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.
