  We report measurements of thermal self-locking of a Fabry-Perot cavity
containing a potassium niobate (KNbO3) crystal. We develop a method to
determine linear and nonlinear optical absorption coefficients in intracavity
crystals by detailed analysis of the transmission lineshapes. These lineshapes
are typical of optical bistability in thermally loaded cavities. For our
crystal, we determine the one-photon absorption coefficient at 846 nm to be
(0.0034 \pm 0.0022) per m and the two-photon absorption coefficient at 846 nm
to be (3.2 \pm 0.5) \times 10^{-11} m/W and the one-photon absorption
coefficient at 423 nm to be (13 \pm 2) per m. We also address the issue of
blue-light-induced-infrared-absorption (BLIIRA), and determine a coefficient
for this excited state absorption process. Our method is particularly well
suited to bulk absorption measurements where absorption is small compared to
scattering. We also report new measurements of the temperature dependence of
the index of refraction at 846 nm, and compare to values in the literature.
