A deep, wide-field, near-infrared imaging survey was used to construct an extinction map of the southeastern part of the California Molecular Cloud (CMC) with $sim$ 0.5 arc min resolution. The same region was also surveyed in the $^{12}$CO(2-1), $^{1
3}$CO(2-1), C$^{18}$O(2-1) emission lines at the same angular resolution. Strong spatial variations in the abundances of $^{13}$CO and C$^{18}$O were found to be correlated with variations in gas temperature, consistent with temperature dependent CO depletion/desorption on dust grains. The $^{13}$CO to C$^{18}$O abundance ratio was found to increase with decreasing extinction, suggesting selective photodissociation of C$^{18}$O by the ambient UV radiation field. The cloud averaged X-factor is found to be $<$X$_{rm CO}$$>$ $=$ 2.53 $times$ 10$^{20}$ ${rm cm}^{-2}~({rm K~km~s}^{-1})^{-1}$, somewhat higher than the Milky Way average. On sub-parsec scales we find no single empirical value of the X-factor that can characterize the molecular gas in cold (T$_{rm k}$ $lesssim$ 15 K) regions, with X$_{rm CO}$ $propto$ A$_{rm V}$$^{0.74}$ for A$_{rm V}$ $gtrsim$ 3 magnitudes. However in regions containing relatively hot (T$_{rm ex}$ $gtrsim$ 25 K) gas we find a clear correlation between W($^{12}$CO) and A$_{rm V}$ over a large (3 $lesssim$ A$_{rm V}$ $lesssim$ 25 mag) extinction range. This suggests a constant X$_{rm CO}$ $=$ 1.5 $times$ 10$^{20}$ ${rm cm}^{-2}~({rm K~km~s}^{-1})^{-1}$ for the hot gas, a lower value than either the average for the CMC or Milky Way. We find a correlation between X$_{rm CO}$ and T$_{rm ex}$ with X$_{rm CO}$ $propto$ T$_{rm ex}$$^{-0.7}$ suggesting that the global X-factor of a cloud may depend on the relative amounts of hot gas within it.
