Understanding the processes occurring during the nanocrystallization of glass-forming liquids is important for creating artificial nanostructures for various applications. In this article, local thermal perturbations in supercooled glass-forming liquids and polymers during the nucleation of a crystalline phase are studied. To describe the thermal response of supercooled glass-forming liquids, an integro-differential heat equation with dynamic heat capacity is used. We have found that the effect of the dynamic heat capacity is significant for fast local thermal perturbations that arise in the early stages of crystal nucleation in glass-forming liquids and polymers. It has been established that local temperature perturbations during the nucleation of crystals in silicate glasses and polymers can change the nucleation rate by 2–5 orders of magnitude. The knowledge gained can be useful for the technology of artificial microstructures and advanced materials.