  We compare the microlensing-based continuum emission region size measurements
in a sample of 15 gravitationally lensed quasars with estimates of
luminosity-based thin disk sizes to constrain the temperature profile of the
quasar continuum accretion region. If we adopt the standard thin disk model, we
find a significant discrepancy between sizes estimated using the luminosity and
those measured by microlensing of
$\log(r_{L}/r_{\mu})=-0.57\pm0.08\,\text{dex}$. If quasar continuum sources are
simple, optically thick accretion disks with a generalized temperature profile
$T(r) \propto r^{-\beta}$, the discrepancy between the microlensing
measurements and the luminosity-based size estimates can be resolved by a
temperature profile slope $0.37 < \beta < 0.56$ at $1\,\sigma$ confidence. This
is shallower than the standard thin disk model ($\beta=0.75$) at $3\,\sigma$
significance. We consider alternate accretion disk models that could produce
such a temperature profile and reproduce the empirical continuum size scaling
with black hole mass, including disk winds or disks with non-blackbody
atmospheres.
