Gas-cooled reactors are among the most promising Generation IV nuclear energy systems, and helium-based binary mixtures are attractive candidate coolants because of their favorable thermophysical and chemical properties. In this work, a numerical investigation was conducted to study the distribution evolution and thermal stratification of a He–Ar gas mixture in a closed cylindrical vessel. The effects of the mixing ratio, initial pressure, vessel aspect ratio, initial temperature, and axial temperature difference on the species distribution were systematically analyzed. The results indicate that the mixing ratio, initial pressure, vessel aspect ratio, and initial temperature exert only minor effects on the overall gas distribution. By contrast, the axial temperature difference is identified as the key factor controlling the onset and intensity of stratification. A larger temperature gradient induces stronger compositional non-uniformity and results in more pronounced axial stratification within the vessel. In addition, temperature non-uniformity further amplifies the stratification process. These results provide a quantitative basis for evaluating composition non-uniformity in closed gas systems. The present study improves the mechanistic understanding of coupled thermal and compositional stratification in confined binary rare-gas mixtures and provides a reference for evaluating similar transport phenomena in gas-cooled nuclear systems.