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We numerically calculated the transient temperature distribution of flowing subcooled liquid nitrogen in a high-Tc superconducting (HTS) model cable when faults occur. The coolant and cable core temperatures were calculated by numerically solving the heat equation using the finite difference method. In the calculation, we assume that the heat transfer coefficient between the flowing subcooled liquid nitrogen and the cable core surface is described by the Dittus-Boelter correlation. The calculation results reveal that the coolant temperature increases even after the fault has been removed and that it continues increasing until fresh coolant arrives from the inlet. The calculated temperature profile of the coolant agrees well with measured data obtained by conducting over-current tests on a model HTS cable. Using our computational code, we also evaluated the maximum HTS cable lengths that ensure that the coolant remains in the liquid phase for certain fault currents for an HTS model cable.