In light of the growing evidence pointing at core-collapse supernovae as large dust producers, and given their immense number in young massive stellar clusters (SSCs), this work is devoted to address the influence of stochastic injection, sputtering and outflow of dust grains on their emission properties inside the hot and dense intracluster medium. The theory of dust radiative cooling, which considers time-dependent dust size distributions and chemical composition, is combined with a self-consistent semi-analytic method, in order to study the hydrodynamics of spherically symmetric winds driven by SSCs with a generalized Schuster stellar density profile.