  We present new mid-IR observations of the quadruply lensed quasar Q2237+0305
taken with CanariCam on the Gran Telescopio Canarias. Mid-IR emission by hot
dust, unlike the optical and near-IR emission from the accretion disk, is
unaffected by the interstellar medium (extinction/scattering) or stellar
microlensing. We compare these "true" ratios to the (stellar) microlensed flux
ratios observed in the optical/near-IR to constrain the structure of the quasar
accretion disk. We find a half-light radius of
$R_{1/2}=3.4_{-2.1}^{+5.3}\sqrt{\langle M \rangle/0.3\,\rm{M_{\odot}}}$
light-days at $\lambda_{rest}=1736$ {\AA}, and an exponent for the temperature
profile $R \propto \lambda^{p}$ of $p=0.79\pm0.55$, where $p=4/3$ for a
standard thin-disk model. If we assume that the differences in the mid-IR flux
ratios measured over the years are due to microlensing variability, we find a
lower limit for the size of the mid-IR-emitting region of $R_{1/2} \gtrsim
200\,\sqrt{\langle M \rangle/0.3\,\rm{M_{\odot}}}$ light-days. We also test for
the presence of substructure/satellites by comparing the observed mid-IR flux
ratios with those predicted from smooth lens models. We can explain the
differences if the surface density fraction in satellites near the lensed
images is $\alpha = 0.033_{-0.019}^{+0.046}$ for a singular isothermal
ellipsoid plus external shear mass model or $\alpha = 0.013_{-0.008}^{+0.019}$
for a mass model combining ellipsoidal NFW and de Vaucouleurs profiles in an
external shear.
