The thermal emission spectra of the metal-backed thin films of NaF have been observed at the emission angle of 30 degrees . The observed spectra measured at elevated temperatures have been analysed by using the response function based on the virtual-mode theory in order to estimate the value of the damping constants around the LO and TO modes. The results yield that the fractional damping around the LO mode is proportional to temperature, while that around the TO mode varies non-linearly with temperature. The lowest order contribution to the phonon self-energy based on the perturbation theory on the anharmonic lattice seems to be dominant to the large damping constant near the LO mode, but the second-lowest order contribution seems to be significant to the small damping constant around the TO mode.