During the operation of the floating ring gas film seal, a certain amount of heat is generated inside the seal gap, giving rise to thermal deformation of the seal rings, and further leading to operation unstable and increased leakage rate. Based on the gas lubrication theory, the control equations of gas pressure and gas film thickness of the floating ring gas film seal are obtained. And the energy and temperature-viscosity equation are also introduced. The above equations were solved by the finite difference method and their correctness was verified by experiments. The variation of opening force, leakage rate, friction force, and gas film temperature rise with rotating speed, inlet pressure, and eccentricity were analyzed. The results reveal that, for leakage rate, the difference between the modeled and tested values is only 2.94% at high speeds, taking into account the influence of the temperature-viscosity effect. The experiment substantiates that the temperature-viscosity effect model is scientifically valid. Operation parameters also have different effects on sealing performance. Compared with isothermal flow, the pressure distribution in the gas film flow field will change significantly with increasing gas temperature, which means that the temperature-viscosity effect cannot be neglected in the flow field calculation. These results provide grounds for further study of the thermoelastic effect of air film seal of floating ring and have important engineering significance.