The position and size of the energy gap in the phonon density of states of NaI single crystal have been investigated by inelastic neutron scattering in a wide range of temperatures from 10 to 700 K. The results reveal a pronounced temperature effect which effectively leads to closure of the phonon gap at temperatures in the range of 700-800 K. The results are discussed in the context of studies of possible intrinsic localized modes in the phonon gap of alkali halides.