Coated conductors are very promising for the design of novel and efficient resistive Fault Current Limiters (FCLs). However, a detailed knowledge about their thermal and electromagnetic behaviors in the presence of over- critical currents is crucial for their improvement. In this context, we performed finite element magneto-thermal modeling of coated conductors under over-critical current on several geometries. Accordingly, we have investigated the influence of the physical properties of stabilizer and substrate on the thermal stability to improve the HTS-FCL design. All simulations were performed using COMSOL Multiphysics, a commercial finite element package, which has a built-in coupling between the thermal and electrical equations, allowing us to compute both quantities simultaneously during the solving process. Our results allow us to determine the current threshold to achieve thermal stability of HTS fault current limiters made with coated conductors.