Temperature rise due to self-heating at very low temperatures near 0.4 K has been numerically estimated for a 2 μm on a side and 3 nm-thick mesa of Bi2Sr2CaCu2O8+δ intrinsic Josephson junctions. In spite of very low thermal conductivities and specific heats of the materials constructing the mesa at these temperatures, the temperature rise is much less than 1 K at a usual current injection level. It is also found that the temperature rise shows a tendency to increase with the mesa size, which was also observed at higher temperatures. The temperature rise in the presence of the contact resistance is also estimated to be small when the contact resistivity is of the order of 1 × 10−10 Ωm2. When the contact resistance is larger, the temperature rise becomes comparable with 1 K. The temperature rise in the presence of a voltage state junction is much less than 1 K at a critical current level. This implies that the saturation of the escape temperature of the recent switching probability experiments is totally unlikely to be due to simple heating characterized by the thermal equilibrium in phonons.
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