The electron-phonon coupling in iron-doped yttrium aluminum garnet crystals is studied in the theoretical framework of linear and quadratic coupling. The line shift and line broadening of the zero phonon line of iron centers as a function of temperature between 10 and 150 K is qualitatively and quantitatively explained. The spectroscopic features of the line, deduced from the theory of lattice relaxation and multiphonon transitions, is compared with experimental results. The perturbation model indicates a linear coupling of medium strength and a strong quadratic coupling, providing an understanding of the thermal properties of spectral lines of ions in solids. The evaluated Huang-Rhys parameter is 2.05 and the quadratic coupling factor is parallel to w parallel to=0.85. The estimated Debye temperature is about 450 K.