The influence of spin-phonon coupling on the specific heat of a system of paramagnetic ions in a lattice, the so-called Schottky anomaly, is calculated using the resolvent operator version of perturbation theory. It is found that this coupling does not cause the sharpening of the Schottky peak observed in cerium ethyl sulphate by Meyer and Smith. This is in conflict with earlier results obtained by Sears and by Tucker using Green function theory. The disagreement is traced to their use of an incorrect decoupling approximation. Finally the lifetimes of coupled spin-phonon modes are calculated.