  Thermal photon production at mid-rapidity in Au+Au reactions at
$\sqrt{s_{NN}}$ = 200 GeV is studied in the framework of a 2D+1 hydrodynamical
model that describes efficiently the bulk identified hadron spectra at RHIC.
The combined thermal plus NLO pQCD photon spectrum is in good agreement with
the yields measured by the PHENIX experiment for all Au+Au centralities. Within
our model, we demonstrate that the correlation of the thermal photon slopes
with the charged hadron multiplicity in each centrality bin provides direct
empirical information on the underlying degrees of freedom and on the equation
of state, $s(T)/T^3$, of the strongly interacting matter.
