  We calculate the spectra of produced thermal photons in Au+Au collisions
taking into account the nonequilibrium contribution to photon production due to
finite shear viscosity. The evolution of the fireball is modeled by
second-order as well as by divergence-type 2+1 dissipative hydrodynamics, both
with an ideal equation of state and with one based on Lattice QCD that includes
an analytical crossover. The spectrum calculated in the divergence-type theory
is considerably enhanced with respect to the one calculated in the second-order
theory, the difference being entirely due to differences in the viscous
corrections to photon production. Our results show that the differences in
hydrodynamic formalisms are an important source of uncertainty in the
extraction of the value of $\eta/s$ from measured photon spectra. The
uncertainty in the value of $\eta/s$ associated with different hydrodynamic
models used to compute thermal photon spectra is larger than the one occurring
in matching hadron elliptic flow to RHIC data.
