The GaAs detectors are radiation hard against a few MGy of high-energy (MeV) electrons. The main reason for detector functionality degradation is the reduction of their charge collection efficiency and together with reverse current increase these facts cause the drop of the signal to noise ratio down to close to 1, disabling detector functionality. In this paper, the lowering of detector temperature has improved the spectra of less ionizing particles, the 59.5 keV gamma rays, measured by semi-insulating GaAs pad detectors, which were first degraded by 8 MeV electrons with a dose of 200 kGy. The signal to noise ratio improved by about 30%, from 1.09 at room temperature up to 1.42 at 276 K. The photo-peak was easily distinguishable from the noise during cooling and the calculated detector relative energy resolution improved from 46% at room temperature to 34% at 276 K. A mild decrease in detector charge collection efficiency was observed, by about 5% of its initial value, when cooling the detector to 276 K.