Light sources such as high-repetition-rate free-electron lasers and low-emittance synchrotron radiation diffraction-limited storage rings place higher demands on the thermal deformations of the mirrors. Given the high average thermal power and the wavefront preservation demand of the Shanghai high repetition rate XFEL and extreme light facility (SHINE), the thermal power distribution on the first mirror named M1 for the first beamline at different energy points is calculated. A finite-element analysis model with thermal and structural coupling is built to calculate the thermal deformation of M1 and conduct wavefront propagation simulation. Finally, the mirror cooling design is optimized by multi-segment cooling and compound utilization. The results show that when the incident light has an energy of 7.0 keV and an grazing angle of 4 mrad, the rated thermal power is improved from 0.48 W to 3.06 W, and the working repetition rate is enhanced by 6.4 times accordingly. According to the optical simulation results, the rated thermal power is also increased by 2.0 to 8.3 times at other energy points.