  Midplane heating induced by disk accretion plays a key role in determining
the disk temperature particularly at the inner disk midplane where planets
form. However, the efficiency of accretion heating has been not well
constrained by observations. We construct two-dimensional models of the Class
II disk around CW Tau, taking into account the midplane heating. The models are
compared with the ALMA dust continuum observations at Bands 4, 6, 7 and 8, with
an angular resolution of 0.1 arcsec. The observed brightness temperatures are
almost wavelength-indenpendent at $\lesssim$10 au. We find that if the maximum
dust size $a_{\rm max}$ is $\lesssim100~{\rm \mu m}$, the brightness
temperatures predicted by the model exceed the observed values, regardless of
the efficiency of accretion heating. The low observed brightness temperatures
can be explained if millimeter scattering reduces the intensity. If the disk is
passive, $a_{\rm max}$ needs to be either $\sim150~{\rm \mu m}$ or $\gtrsim$
few ${\rm cm}$. The accretion heating significantly increases the brightness
temperature particularly when $a_{\rm max}\lesssim300~{\rm \mu m}$, and hence
$a_{\rm max}$ needs to be either $\sim300~{\rm \mu m}$ or $\gtrsim$ few ${\rm
cm}$. The midplane temperature is expected to be $\sim$1.5-3 times higher than
the observed brightness temperatures, depending on the models. The dust
settling effectively increases the temperature of the dust responsible for the
millimeter emission in the active disk, which makes the model with $300~{\rm
\mu m}$-sized dust overpredicts the brightness temperatures when strong
turbulence is absent. Porous dust (porosity of 0.9) makes the accretion heating
more efficient so that some sort of reduction in accretion heating is required.
Future longer wavelength and higher angular resolution observations will help
us constrain the heating mechanisms of the inner protoplanetary disks.
