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We investigate ferroelectric random access memories subjected to X-ray and proton irradiations. We address the radiation damage dependence on irradiation temperature, its stability during annealing and cycling, and the effects of supply voltage and packaging. The radiation damage strongly depends on the irradiation temperature. Immediately after proton or X-ray irradiation, we detect only stuck bits without data corruption, at least at doses up to 9 Mrad(Si) at room temperature. The radiation damage anneals in time as long as several weeks, and the recovery rate is accelerated by either electrical cycling or high temperature annealing. The radiation tolerance is much higher if the device is irradiated unpowered. Finally, we present a degradation model that accounts for the irradiation temperature dependence.