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Various kinds of superconductivity-based fault current limiters (FCL's) have been studied. One type uses a superconductive reactor or magnet that loses its superconductive properties when subjected to excessive current flow. We examined the characteristics of a Bi2223 double pancake coil subjected to overcurrent. DC or AC overcurrent was passed through the coil cooled by saturated liquid nitrogen, and the resultant temperature difference was measured between the coil surface and the saturated liquid nitrogen. We then theoretically and experimentally investigated the starting conditions of the resultant thermal runaway. Our results confirmed that these conditions are decided by the product of critical heat flux and cooling area, and that the angle of the coil is important if the cooling channels are narrow.