  We present the results of a long-term observation campaign of the
extragalactic wind-accreting black-hole X-ray binary LMC X-1, using the
Proportional Counter Array on the Rossi X-Ray Timing Explorer (RXTE). The
observations show that LMC X-1's accretion disk exhibits an anomalous
temperature-luminosity relation. We use deep archival RXTE observations to show
that large movements across the temperature-luminosity space occupied by the
system can take place on time scales as short as half an hour. These changes
cannot be adequately explained by perturbations that propagate from the outer
disk on a viscous timescale. We propose instead that the apparent disk
variations reflect rapid fluctuations within the Compton up-scattering coronal
material, which occults the inner parts of the disk. The expected relationship
between the observed disk luminosity and apparent disk temperature derived from
the variable occultation model is quantitatively shown to be in good agreement
with the observations. Two other observations support this picture: an inverse
correlation between the flux in the power-law spectral component and the fitted
inner disk temperature, and a near-constant total photon flux, suggesting that
the inner disk is not ejected when a lower temperature is observed.
