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We developed a computer code to analyze the stability of a superconducting wire in He II based on the one-dimensional heat equation. We applied to this code our experimental data on heat transfer characteristics of He II, such as Kapitza conductance, critical heat flux and heat transfer curve in film boiling. Using this code, we simulated the recovery or quench process of a normal zone that was initiated by a thermal disturbance for the liquid helium temperatures from 1.8 K to 2.0 K at atmospheric pressure. The numerical solutions agreed with our experimental data for the same characteristics of the wire (bare and oxidized surfaces) and corresponding experimental conditions. We clarified the influences of the surface insulation and the liquid helium temperature on the stability of the superconducting wire.