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It is known that MgB2-based strands may be used in fault current limiters as a low-cost alternative to high-temperature YBCO coated conductors. Numerical modeling of the ac limiting properties of MgB2 strands with Kapton insulation and conduction cooling have been performed using a finite element method. Two 2D ac Poisson equations, one for calculating the electric field and one for determining the heat transfer were solved simultaneously with input parameters taken from experimental results. As boundary conditions, we took the full non-linear curve of the heat flux into a cryocooler cold head as well as heat radiation from the free surfaces of the wire. The influence of different values and durations of fault electric fields were studied and the maximum temperatures, limiting currents and recovery times were calculated. Obtained results may be useful for understanding the behavior of different kinds of MgB2 multifilamentary wires under conditions encountered in fault current limiter devices.