Diamond crystals not only have excellent optical properties, but also have extremely high thermal conductivity and low thermal expansion coefficient, which makes diamond laser an important path to achieve high-power laser output without heat. However, with the further increase of laser power, thermal effects that cannot be ignored in diamond Raman lasers (DRLs), which poses a challenge to the performance improvement of diamond lasers. The thermal effect of the DRLs under high power operation was studied theoretically. Based on the thermal conduction equation and finite element analysis method, the temperature, thermal stress and thermal deformation distribution of diamond were simulated, and the effects of pump and crystal parameters on the above factors were analyzed. Moreover, a novel heat sink structure for diamond was designed based on the transverse thermal conductivity characteristics of graphite sheets. Compared with traditional heat dissipation methods of single copper-sheet, under the pump power of 800 W and waist radius of 40 μm, the center temperature of the diamond was reduced by 10.16 K, the average stress on the lower surface was reduced by 19.857 MPa, and the average deformation of the end face was reduced by 0.055 μm. The numerical simulation results show that this method has important guiding significance for mitigating the thermal effect of diamond laser, further enhancing the output power of DRLs and achieving high beam quality laser output.