  By fitting synthetic spectral models computed via the TLUSTY code, we examine
how the spectra from thin accretion disks are expected to vary in accreting
black hole systems. We fit color-corrected blackbody models to our synthetic
spectra to estimate the spectral hardening factor f, which parameterizes the
departure from blackbody and is commonly used to help interpret
multitemperature blackbody fitting results. We find we can define a reasonably
robust f value to spectra when the effects of Compton scattering dominate
radiation transfer. We examine the evolution of f with black hole mass and
accretion rate, typically finding a moderate variation (f ~ 1.4-2) for
accretion rates between 1% and 100% of the Eddington rate. Consistent with most
previous work, we find f tends to increase with accretion rate, but we also
infer a weaker correlation of f with black holes mass. We find that f is rarely
much larger than 2 unless the disk becomes photon starved, in contention with
some previous calculations. Significant spectral hardening (f > 2) is only
found when the disk mass surface density is lower than expected for alpha-disk
models unless alpha is near unity or larger.
