Avalanche photodiodes have been chosen as photon sensors for the electromagnetic calorimeter of the CMS experiment at the LHC. These sensors should operate in the 4 T magnetic field of the experiment. Because of the high neutron radiation in the detector extensive studies have been done by the CMS collaboration on the APD neutron radiation damage. The characteristics of these devices after irradiation have been analyzed, with particular attention to the quantum efficiency and the dark current. The recovery of the radiation-induced dark current has been studied carefully at room temperature and at slightly lower and higher temperatures. The temperature dependence of the annealing has been evaluated.