Abstract: High-energy and high-intensity proton accelerators in the range of several MW are widely applied in the fields of the nuclear industry, civil applications and fundamental researches. In this scenario, a high power circular accelerator complex consisting of a 100 MeV pre-injector cyclotron, a 800 MeV injector ring cyclotron and a 2 GeV continuous wave (CW) fixed field alternating gradient accelerator (FFA) was proposed at China Institute of Atomic Energy. The development of the 44.4 MHz high power waveguide type RF cavity with high quality factor and high shunt impedance is extremely important for 2 GeV CW FFA. In order to acquire the fabrication technology and operation experience of the boat shape cavity, R&D on a 177.6 MHz quarter scaled prototype cavity was conducted. The power dissipated on the prototype surface can reach hundreds of kW, resulting in thermal stress of the cavity. Under the combined action of thermal stress, gravity, atmospheric pressure and mechanical constraint, the cavity frequency shifts. Therefore, it is necessary to resist the deformation of the cavity through various measures such as cooling water and changing the external forces on the cavity, and adjust the frequency to the design range. Solid-thermal coupling method and fluid-solid-thermal coupling method were used to carry out the multi-physical simulation of the cavity respectively, and the distribution of power loss in the surface, temperature field, stress field and deformation field of the boat shape cavity was calculated in the process. The effect of different force and the influence of the deformation of the cavity on the frequency were analyzed. The result by the fluid-solid-thermal coupling method shows that the cavity temperature near the inlet area is lower than that in the outlet area. However, the results calculated by solid-thermal coupling method show that the cavity temperature distribution on the two regions is almost equal. The above results show that the fluid-solid-thermal coupling method are more consistent with the actual physical process. The temperature field distribution obtained by the two methods has slightly different influence on the deformation field and the frequency adjustment range, but the solid-thermal coupling method requires less computer configuration, simpler model processing and slightly faster calculation speed. For the quarter scaled cavity, the results obtained by the two thermal simulation methods are generally consistent, and the solid-thermal coupling simulation methods in practical application are sufficient to meet the requirements of engineering design.