To address the local thermal damage at the rail exit end induced by muzzle arc during the armature muzzle-exit stage of an electromagnetic rail launcher, an equivalent heat-input prediction method based on measured electrical parameters is established. The armature exit time and muzzle-arc action interval are determined using the rail current, muzzle voltage, B-dot probe velocity measurement, and light-screen velocity measurement. The instantaneous arc power and equivalent input energy are reconstructed from the abnormal muzzle voltage and residual current. The reconstructed energy is then converted into a three-dimensional heat-flux boundary with spatial concentration and temporal transience, and a transient heat-conduction model of the rail exit end is developed. The calculated results show that the muzzle arc can raise the temperature near the inner edge and groove region of the rail exit end to approximately 1140–1180 °C, exceeding the melting point of the copper alloy. The melting/ablation risk zone is mainly concentrated in the surface layer close to the armature motion channel. Along the depth direction, the temperature decreases rapidly and drops below 200 °C at a depth of about 1.8 mm. The simulated peak temperature and high-temperature distribution are in good agreement with the infrared temperature measurement and post-launch ablation morphology. The results indicate that the muzzle arc is an important factor causing local thermal damage at the rail exit end. The proposed method can provide a reference for rail-end thermal protection design, structural optimization, and repeated-launch reliability assessment of electromagnetic rail launchers.