  Lattice data on QCD thermodynamics, especially recent study of high order
susceptibilities by UK-Bielefeld collaboration, have provided valuable
information about matter properties around and above the critical temperature
$T_c$. In this work we tried to understand what physical picture would explain
these numerical data. We found two scenarios which will do it: (i) a quark
quasiparticle gas, with the effective mass which is strongly $decreasing$ near
the phase boundary into the QGP phase; or (ii) a picture including baryons at
$T>T_c$, with the mass rapidly $increasing$ across the phase boundary toward
QGP. We further provide several arguments in favor of the latter scenario, one
of which is a natural continuity with the baryon gas picture at $T<T_c$.
