The purpose of this study is to investigate the temperature condition for distributing the residual moment efficiently along the irradiation direction in a thin metal plate when a laser beam is irradiated to the surface of the plate with cooling its back side. In our previous study, it was revealed that the residual moment cannot be distributed largely and widely only by conducting the first multi-point irradiation. Therefore, it is necessary to examine overlapping irradiation that is performed by irradiating once again after conducted the first multi-point irradiation. Especially, the distributions of the residual moment generated under the overlapping irradiation are examined by changing the conditions of irradiation temperature and irradiation distance. Then, the effect of temperature condition on the distribution of the residual moment is revealed in this research.