Thin films are very promising for the design of novel and efficient Fault Current Limiter (FCL) made of high-temperature superconductors (HTS). However, their thermal and highly non-linear electromagnetic behavior in the presence of over-critical currents is crucial to their use in future electrical grid. In this paper, we propose a numerical approach to solve magneto-thermal models for geometries of high aspect ratio. The used electromagnetic formulation, inspired in good part from the work of Brambilla et al., were performed in 2D using COMSOL Multiphysics. Also, the thermal part of our model has been implemented to consider the thermal exchange with the nitrogen bath needed for HTS-FCL operation. Our simulations allow us to observe design limitations of FCL made of these new shaped conductors.