The nuclear spin-lattice relaxation time T1 has been measured in NaF, KBr, KI, NaI, and LiBr at temperatures ranging from 20-800°K to determine the sensitivity of T1 to changes in the lattice vibrational spectrum and the relative importance of acoustic and optic phonons for quadrupolar relaxation. The theoretical temperature dependence for T1 derived by Van Kranendonk for two-phonon Raman processes using a Debye spectrum does not fit the data for all crystals. The discrepancies are attributed to the importance of optic phonons for quadrupolar relaxation in crystals having large mass ratios. Different temperature dependences are expected for relaxation arising from acoustic and optic phonons. A simple temperature dependence for T1 obtained by approximating the frequency distribution of the acoustic vibrations by a Debye spectrum and the optic vibrations by an Einstein spectrum is discussed and applied to the data for KI and NaI.