We investigated offline the evolution of radiation-induced attenuation (RIA) in polymer perfluorinated cyclic transparent optical polymer (CYTOP) optical fiber irradiated with different gamma radiation doses of 1–50 kGy. We considered the wavelength range varying from 800 up to 1750 nm. The RIA spectra measured at different times after irradiation have qualitatively similar shapes. However, quantitatively the RIA evolution significantly depends on the spectral range: in the short-wavelength part, the transmission partly recovers, while in the infrared, at wavelengths above 1300 nm the RIA grows and then saturates becoming permanent. The effects of temperature and photobleaching on RIA dynamics are examined. The ability of the fiber transmission recovery is investigated in the 600–1750-nm range with the use of climatic chamber.