  Blast wave fits are widely used in high energy nuclear collisions to capture
essential features of global properties of systems near kinetic equilibrium.
They usually provide temperature fields and collective velocity fields on a
given hypersurface. We systematically compare blast wave fits of fluid dynamic
simulations for Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV and Pb+Pb
collisions at $\sqrt{s_{NN}}=2.76$ TeV with the original simulations. In
particular, we investigate how faithful the viscous blast wave introduced in
\cite{Yang:2022yxa} can reproduce the given temperature and specific shear
viscosity fixed at freeze-out of a viscous fluid dynamic calculation, if the
final spectrum and elliptic flow of several particle species are fitted. We
find that viscous blast wave fits describe fluid dynamic pseudodata rather well
and reproduce the specific shear viscosities to good accuracy. However,
extracted temperatures tend to be underpredicted, especially for peripheral
collisions. We investigate possible reasons for these deviations. We establish
maps from true to fitted values. These maps can be used to improve raw fit
results from viscous blast wave fits. Although our work is limited to two
specific, albeit important, parameters and two collision systems, the same
procedure can be easily generalized to other parameters and collision systems.
