The hot image effect of the high power laser system may cause the peak power of the beam to increase drastically, and the amplifying Keer medium will make this increase in light intensity more intense. When the input beam power is strong enough, the gain saturation effect of the amplifying Keer medium on the beam is more obvious. Based on the Fresnel-Kirchhoff diffraction theory and the nonlinear paraxial wave equation, the hot image generation process of the intense laser in the gain saturation region of the amplifying Keer medium is theoretically analyzed, and the gain saturation part of the beam transmission equation is subjected to the Maclaurin expansion for approximation. After deriving the analytical formula of hot image intensity and hot image position when the medium is thin, the hot image intensity and position predicted by the analytical conclusion are verified by numerical simulation. The simulation results show that the position of the hot image is symmetrical to the diffracted object with respect to the medium, and the analysis results of hot image intensity are consistent with the simulation results. The intensity of the hot image stops increasing as the nonlinear effect of the nonlinear medium increases. In addition, the change of the intensity of the hot image with the obscuration type is discussed.