  The effects of gravitational darkening on the thermal structure of Be star
disks of differing densities are systematically examined. Gravitational
darkening is the decrease of the effective temperature near the equator and the
corresponding increase near the poles of a star caused by rapid rotation. We
also include the rotational distortion of the star using the Roche Model.
Increasing the disk density increases the optical depths in the equatorial
plane, resulting in the formation of an inner cool region near the equatorial
plane of the disk. High rotation rates result in disks that have temperatures
similar to those of a denser disk, namely cooler overall. However the effect of
increasing rotation produces additional heating in the upper disk due to the
hotter stellar pole. Cool regions in the equatorial plane normally associated
with high density are seen in low density models at high rotation rates.
Gravitational darkening increases the amount of very cool and very hot material
in the disk and decreases the amount of disk material at moderate temperatures.
We also present models which study the effect of gravitational darkening on
hydrostatically-converged disks, in which the temperature structure is
consistent with vertical hydrostatic equilibrium. Because the equatorial
regions become cooler, hydrostatically converged models that include gravity
darkening have smaller vertical scale heights, and $H/R$ is smaller by as much
as 56% near $v_{\rm crit}$. Finally we explore differences in disk temperatures
when alternate formulations of gravitational darkening, which lower the
temperature difference between the pole and the equator, are used.
