Based on the no aberration self-focusing theory, under the condition of the optical thin and far field approximation, hot-image effect formed when the space chirp gaussian beams pass through free space and nonlinear medium was studied using analytical and numerical simulation methods, respectively. The influence of the chirp parameter on the nonlinear hot image was discussed. Results show that the chirp parameter has a great influence on nonlinear hot-image position and strength. Nonlinear hot-image strength can be largely inhibited by negative chirp and small-bore gaussian beam. Moreover, hot-image position can be changed by adjusting the chirp parameter C, making it deviated from the downstream of the optical element and ensuring the safe operation of the optical system.