For a realistic aggregate grown under the diffusion control, the fractal scaling holds between two cutoff lengths. These cutoff lengths often control the dynamics of aggregation and relaxation. During thermal annealing, coarsening of the aggregate structure takes place, and the lower cutoff length increases. When the relaxation is limited by kinetics, we show by a simple dimensional argument that the perimeter length (or area) A of the aggregate shrinks in a power law with time t as A(t) ~ t(d–1–D)/2 in a d-dimensional space, where D is the fractal dimension of the aggregate. This prediction is tested by Monte Carlo simulation of the thermal relaxation of a two-dimensional diffusion-limited aggregation.