Relaxation through phonon exchange of adsorbates on the surface of a crystal is considered. The effect of the thermal phonon field on the time evolution of the adsorbate is taken into account with finite-memory-time reservoir theory. Also, the low-intensity photon absorption profile is evaluated. The spectrum has a sharp cutoff at the Debye frequency ω_D of the crystal and a memory-induced extra resonance at ω_D+ω_O, where ω_O is an adsorbate transition frequency. Both features of the profile are explained in physical terms.