The fuel rods in high temperature gas reactor face a great axial temperature gradient, and the heat transfer of pellets will change the material characteristics of the fuel rods on the one hand. On the other hand, the gas has obvious thermal expansion under the influence of a heat source, which makes the fluid structure interaction of the fuel rods more complicated. In order to study the dynamic stability of fuel rods excited by high-temperature and high-speed axial gas, the spatial temperature distribution of fuel rod cladding is solved, and the thermodynamic coupling control equation of fuel rods was derived. The instability boundary of the fuel rod is defined by using the eigenvalue distribution of Jacobian matrix, and the effects of the maximum heat source line power density, inlet temperature and thermal expansion on the first critical mass flow rate of the fuel rod are obtained. The results show that the maximum heat source line power density has little influence on the first critical mass flow rate of the fuel rods, and the higher the inlet temperature, the smaller the first critical mass flow rate. Considering the thermal expansion of gas, the maximum heat source line power density and inlet temperature are negatively related to the first critical mass flow rate. If the thermal expansion effect of gas is not considered, the first critical mass flow rate of fuel rod will be overestimated.