The Brayton cycle system has a wide range of applications, including ship waste heat utilization, space reactors, sodium-cooled fast reactors, megawatt nuclear power systems and aerospace. The circulating temperature and circulating medium also vary with the specific application environment. The heat source temperature is usually between 700 K and 2,100 K. The commonly used working medium includes SCO2, helium and nitrogen. At present, the research and analysis of some parameters in a given working fluid and temperature are applied to specific engineering. According to the environment temperature and working medium, based on MATLAB software, the numerical model of the Brayton cycle under different working conditions is established. In addition, other calculation software is used for programming calculation to obtain the analysis results of temperature change conditions and the comparison of different conditions, providing reference and selection basis for the application of Brayton cycle in practical engineering, so that the most suitable Brayton cycle working medium and cycle model can be selected under specific conditions. The influence of changing the heat exchanger into phase change heat exchanger on the instability of the heat source is analyzed. In this paper, the thermal efficiency curves between 716 K and 2,116 K of the heat source of Brayton cycle for helium, SCO2 and nitrogen under four different cycle efficiencies were calculated, and the thermal efficiency curves of Brayton recompression cycle for helium, SCO2 and nitrogen under different extraction ratios were calculated. And the temperature changes of four different models in three working media (helium, nitrogen and SCO2) with thermal cycle efficiency were compared.