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 $log(r_{L}/r_{mu})=-0.57pm0.08,text{dex}$. 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.
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