  It was recently discovered that the temperature in the surface layer of
externally heated optically thick gray dust clouds increases with the optical
depth for some distance from the surface, as opposed to the normal decrease in
temperature with distance in the rest of the cloud. This temperature inversion
is a result of efficient absorption of diffuse flux from the cloud interior by
the surface dust exposed to the external radiation. A micron or bigger size
grains experience this effect when the external flux is of stellar spectrum. We
explore what happens to the effect when dust is a mixture of grain sizes
(multigrain). Two possible boundary conditions are considered: i) a constant
external flux without constrains on the dust temperature, and ii) the maximum
dust temperature set to the sublimation temperature. We find that the first
condition allows small grains to completely suppress the temperature inversion
of big grains if the overall opacity is dominated by small grains. The second
condition enables big grains to maintain the inversion even when they are a
minor contributor to the opacity. In reality, the choice of boundary condition
depends on the dust dynamics. When applied to the physics of protoplanetary
disks, the temperature inversion leads to a previously unrecognized disk
structure where optically thin dust can exist inside the dust destruction
radius of an optically thick disk. We conclude that the transition between the
dusty disk and the gaseous inner clearing is not a sharp edge, but rather a
large optically thin region.
