A kinetic model for the diffusion-controlled annealing of excess vacancies under the experimentally relevant, non-isothermal condition of time-linear heating is presented and applied to dilatometry. The evolution of the vacancy concentration with time is quantitatively analyzed, considering as ideal sinks either dislocations or grain boundaries of spherical- or cylindrical-shaped crystallites. The validity of the model is tested using dilatometry data that were obtained for ultrafine-grained Ni prepared by high-pressure torsion. The entire two-stage annealing curve of the dilatometric length change can be analyzed by combining the present kinetic model of vacancy annealing at grain boundaries with established non-isothermal kinetics of recrystallization.