This paper presents a coupled electromagnetic and thermal analysis of single-phase isolated circular high-current busducts as well as gas-insulated transmission lines (GIL). The mathematical model includes the electromagnetic coupling between all present phase conductors and shields of the observed system, taking into account the effect of proximity and the skin effect, and as a result gives the complete distribution of current by phase conductors and shields. It is based on the application of the partial conductor method in combination with the current loop method. Furthermore, the model simultaneously combines the electromagnetic calculation of the current distribution and power losses of the damaged transmission system with the calculation of the temperature rise of the phase conductors and armor. In doing so, the influence of material properties (electrical conductivity, thermal coefficients, emission coefficients) as well as ambient influence (ambient temperature, influence of wind and solar radiation) is taken into account. The application of the model on a specific calculation example is shown.