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We designed and fabricated a 1 T cryocooler-cooled oxide superconducting pulsed coil with Bi2223 multifilamentary flat wires. Previously we studied temperature dependence of the thermal runaway current of the pulsed coil in dc operation. The thermal runaway current was higher than the critical current that was defined as the current where the electric field 10-4 V/m was generated on average over the whole length of the conductor. In this paper, we studied the coil temperature and the ac loss dependence of the thermal runaway current in ac operation. We operated the coil at 0.5 to 5 Hz with a sinusoidal-waveform transport current. The initial coil temperature was set between 30 and 100 K. The thermal runaway current decreased monotonically with increasing temperature in a similar way to dc operation. However, in a low temperature region, the thermal runaway current was restricted to a lower level than that in dc operation due to the ac loss. We discuss the frequency dependence of thermal runaway current in ac operation.