  An approach to account for the effect of thermal lattice vibrations when
calculating exchange coupling parameters is presented on the basis of the KKR
(Korringa-Kohn-Rostoker) Green function method making use of the alloy analogy
model. Using several representative systems, it is shown that depending on the
material the effect of thermal lattice vibrations can have a significant impact
on the isotropic exchange as well as anisotropic Dzyaloshinskii-Moriya
interactions (DMI). This should lead in turn to an additional contribution to
the temperature dependence of the magnetic properties of solids, which cannot
be neglected in the general case. As an example, we discuss such an influence
on the critical temperature of various magnetic phase transitions. In
particular, in the case of skyrmion hosting materials, a strong impact of
lattice vibrations on the DMI is an additional source for temperature dependent
skyrmion stability which should be taken into consideration.
