X-ray spectroscopy is a widely used means of diagnosing densities and temperature within laser-produced plasmas. At X-ray energies above approximately 1 keV, Bragg crystal spectrometers are routinely used to record X-ray spectra. Quantitative measurements of plasma conditions can be obtained with a knowledge of crystal reflectivity and film or detector response. In such data analysis it is always assumed that the crystal response is constant in time. However, we show that under certain adverse experimental conditions the X-ray fluxes incident on the crystal are so high as to significantly transiently modify the reflection characteristics of the crystal. Such degradation need not necessarily be accompanied by a loss of observed spectral solution. The transient (nanosecond-time-scale) change in crystal reflectivity is due to a change from dynamical to more kinematic diffraction caused by an X-ray-induced thermal strain gradient in the surface layer of the crystal. The decay time of this strain is typically several nanoseconds. Calculations of some specific crystal reflectivities and rocking curves under such conditions are presented, and methods of minimizing the effect by appropriate filtering are discussed.