  The temperature structure of protoplanetary disks provides an important
constraint on where in the disks rocky planets like our own form. Recent
nonideal magnetohydrodynamical (MHD) simulations have shown that the internal
Joule heating associated with magnetically driven disk accretion is inefficient
at heating the disk midplane. A disk temperature model based on the MHD
simulations predicts that in a disk around a solar-mass young star, the water
snow line can move inside the current Earth's orbit within 1 Myr after disk
formation. However, the efficiency of the internal Joule heating depends on the
disk's ionization and opacity structures, both of which are governed by dust
grains. In this study, we investigate these effects by combing the previous
temperature model for magnetically accreting disks with a parameterized model
for the grain size and vertical distribution. Grain growth enhances the gas
ionization fraction and thereby allows Joule heating to occur closer to the
midplane. However, growth beyond 10 $\rm \mu m$ causes a decrease in the disk
opacity, leading to a lower midplane temperature. The combination of these two
effects results in the midplane temperature being maximized when the grain size
is in the range 10-100 $\rm \mu m$. Grain growth to millimeter sizes can also
delay the snow line's migration to the 1 au orbit by up to a few Myr. We
conclude that accounting for dust growth is essential for accurately modeling
the snow line evolution and terrestrial planet formation in magnetically
accreting protoplanetary disks.
