  We present a progress report on our investigation of the thermodynamics of
QCD with $N_f=2$ flavors of dynamical Wilson fermions in the limit of a large
number of colors $N_c$. To date, studies of the thermodynamics of QCD at large
$N_c$ have been limited to the quenched approximation, i.e., to the behavior of
pure $\mathrm{SU}(N_c)$ gauge theory at large $N_c$. This is the first study of
thermodynamics at large $N_c$ using dynamical fermions, and thus the first
study able to test whether the quenched approximation is a valid way to
investigate large $N_c$ thermodynamics. After reviewing 't Hooft's large $N_c$
limit, we discuss the automation we use to make this study feasible, and
finally compare our preliminary physics results for $\mathrm{SU}(3-5)$ with
large $N_c$ expectations.
