In the last years there has been a considerable increase in electricity consumption and generation from renewable sources, especially wind and solar photovoltaic. This phenomenon has increased the risk of line saturation with the consequent need of increasing the capacity of some power lines. Considering the high cost and the time involved in installing new power lines, the difficulty in acquiring tower sites and the related environmental impacts, some countries are considering to replace conventional conductors with HTLS (High-Temperature Low-Sag) conductors. This is a feasible and economical solution. In this paper a numerical-FEM (Finite Element Method) approach to simulate the temperature rise test in both conventional and high-capacity substation connectors compatible with HTLS technology is presented. The proposed coupled electric-thermal 3D-FEM transient analysis allows calculating the temperature distribution in both the connector and the conductors for a given current profile. The temperature distribution in conductors and connectors for both transient and steady state conditions provided by the proposed simulation method shows good agreement with experimental data.