Thermal blooming has great influence on high power laser propagation in the atmosphere. It is very important to find a sacling law to evaluate the performance of adaptive optics compensation for the high power laser propagation in the atmosphere. Adaptive optics system with different spatial bandwidths has been simulated and phase compensation for focused beam under thermal blooming with different transmitter apertures and propagation lengths has been numerically calculated by four-dimensional propagation codes. The results show that the spatial resolution of adaptive optics system has little influence on the target beam quality. The target beam quality can be scaled by the thermal distortion parameter N.