We show that the process of evolution of hadronic matter into eventual 'particlization' can be accounted for within a framework that recently led us to a rather unconventional explanation of the solar emission lines in the soft X-ray region. Specifically, we attempt a microscopic description of meson formation in a macroscopic background by using the finite-temperature propagators for q and (q) over bar in a Bethe-Salpeter equation with a Coulomb plus a linear kernel. The equation thus obtained is reduced to a Schrodinger-like equation in the ladder and instantaneous approximations and solved numerically to yield bound-state spectra of the b (b) over bar and c (c) over bar systems. Our results are in reasonably good agreement with the observed masses of the Upsilonium and the Charmonium families.