Considering the increase of the fault current level in electrical network, the current limiters become very interesting. The superconducting limiters are based on the quasi-instantaneous intrinsic transition from superconducting state to normal resistive one. Without detection of default or given order, they reduce the constraints supported by electrical installations above the fault. To avoid the destruction of the superconducting coil, the temperature must not exceed a certain value. Therefore the design of a superconducting coil needs the simultaneous resolution of an electrical equation and a thermal one. This papers deals with a resolution of this coupled problem by the method of Monte-Carlo. This method allows us to calculate the evolution of the resistance of the coil as well as the current of limitation. Experimental results are compared with theoretical ones.