  The effect of gravitational darkening on models of the thermal structure of
Be star disks is systematically studied for a wide range of Be star spectral
types and rotation rates. Gravitational darkening causes a reduction of the
stellar effective temperature towards the equator and a redirection of energy
towards the poles. It is an important physical effect in these star-disk
systems because the photoionizing radiation from the central B star is the main
energy source for the disk. We have added gravitational darkening to the bedisk
code to produce circumstellar disk models that include both the variation in
the effective temperature with latitude and the non-spherical shape of the star
in the calculation of the stellar photoionizing radiation field. The effect of
gravitational darkening on global measures of disk temperature is generally
significant for rotation rates above 80% of critical rotation. For example, a
B0V model rotating at 95% of critical has a density-averaged disk temperature
\approx 2500 K cooler than its nonrotating counterpart. However, detailed
differences in the temperature structure of disks surrounding rotating and
non-rotating stars reveal a complex pattern of heating and cooling. Spherical
gravitational darkening, an approximation that ignores the changing shape of
the star, gives good results for disk temperatures for rotation rates less than
\approx 80% of critical. However for the highest rotation rates, the distortion
of the stellar surface caused by rotation becomes important.
