[en] If the part of the HTS magnet is exposed to the outside of the cryogenic coolant due to the fluctuation of the height of the cooling liquid or the vapor generation, the uncooled part becomes very unstable. In this paper, the unstable equilibrium temperature distribution of the uncooled part of a superconductor is obtained, and the maximum temperature and energy are calculated as a function of the uncooled length. Similar to the superconductor stability problem, the current sharing model was applied to derive the theoretical formula and calculated by numerical integration. We also applied a jump model, which assumes that joule heat is generated in all of the uncooled segment, and compares it with the current sharing model results. As a result of the analysis, the stable equilibrium state and the critical uncooled length in the jump model are not shown in the current sharing model. The stability of the conductors to external disturbances was discussed based on the obtained temperature distribution, maximum temperature, and energy