The formation of Cottrell atmospheres can change the scattering of phonons by dislocations and affect the lattice thermal resistivity due to dislocations. Since diffusion of solute atoms is required to form atmospheres, they are not formed instantaneously. Changes due to annealing are similarly time dependent. The diffusion equation is solved in its Fourier‐inverted form, and changes in phonon scattering and lattice thermal conductivity are obtained in a simple form. Changes in lattice thermal conductivity at higher temperatures occur faster, since diffusion through shorter distances is involved. Diffusion coefficients can be determined by studying the time dependence of the lattice thermal conductivity on annealing, and for slow diffusion this method may have advantages.