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Quench properties of Bi2Sr2CaCu2O8/AgMg tape were experimentally investigated under a cryocooled condition in high magnetic fields. The critical current (Ic), quench current (Iq), and minimum quench energy (MQE) were measured at various initial temperatures of 4.2 K, 10 K, and 20 K and at magnetic fields of 7 T and 9 T. MQE was the minimum disturbance energy enough to make thermal quench and was evaluated from the input energy by a resistive heater. It was found that MQE exhibited the minimum value around 20 K. The temperature margin, difference between the initial temperature and the thermal runaway temperature, decreased monotonously with increase at the operating temperature. Since the temperature dependence of MQE did not agree with that of temperature margin, we focused on the internal energy calculated by integrating specific heat of the sample. The temperature dependence of the internal energy was in agreement with that of MQE qualitatively.