<p>Gas-insulated Metal Transmission Line (GIL) represents a promising alternative to traditional overhead lines for long-distance electric power transmission. The thermal performance of GIL is crucial in determining the dielectric strength of materials, which subsequently affects both transmission capacity and security. In this study, a three-dimensional numerical model is introduced to analyze the coupled relationship between the flow field and temperature field of the environmentally friendly insulating gas perfluoroisobutyronitrile (C₄F₇N). The temperature and flow characteristics of C₄F₇N are analyzed at different Rayleigh numbers. Besides, the effect of GIL geometric size on the flow dynamics and temperature distribution are discussed. The results reveal that the enhancement of buoyancy convection contributes to the temperature drop of conducting body, which enhances the buoyancy convection in return. When the Rayleigh number is below 5 × 10⁵, the flow in GIL is weak and there is only slight variation in temperature of C₄F₇N along the lengthwise direction. However, as the Rayleigh number rises to 5 × 10⁵, the convection become pronounced and distinct variations in temperature distribution along GIL appears. When the Rayleigh number exceeds a threshold value of 1 × 10⁷, the flow instability occurs, leading to an asymmetric temperature distribution as well as the overall temperature drop along GIL. The maximum velocity occurs near the surface of the conduction. As the increase of radius ratio between inner and outer annular surface, both flow intensity strengthens and noticeable reductions in temperature become more apparent. These findings can be utilized for insulation design considerations within GIL systems.</p>