In this work we present the results of the experimental studies of the dependence of the X-ray radiation on the temperature change speed of the lithium tantalate monocrystal in the pyroelectric source of the X-ray radiation. We have found an optimized linear temperature speed change pattern for the pyroelectric crystal designed for generation of the X-ray radiation with enhanced capabilities. The studies that were made open an opportunity to determine the most convenient conditions for generation of X-ray radiation with pyroelectric effect and for development of high-capacity pyroelectric X-ray radiation sources.