We construct a theoretical model for low-temperature crystallization of amorphous silicate grains induced by exothermic chemical reactions. As a first step, the model is applied to the annealing experiments, in which the samples are (1) amorphous silicate grains and (2) amorphous silicate grains covered with an amorphous carbon layer. We derive the activation energies of crystallization for amorphous silicate and amorphous carbon from the analysis of the experiments. Furthermore, we apply the model to the experiment of low-temperature crystallization of an amorphous silicate core covered with an amorphous carbon layer containing reactive molecules. We clarify the conditions of low-temperature crystallization due to exothermic chemical reactions. Next, we formulate the crystallization conditions so as to be applicable to astrophysical environments. We show that the present crystallization mechanism is characterized by two quantities: the stored energy density Q in a grain and the duration of the chemical reactions tau. The crystallization conditions are given by Q > Q(min) and tau < tau(cool) regardless of details of the reactions and grain structure, where tcool is the cooling timescale of the grains heated by exothermic reactions, and Q(min) is minimum stored energy density determined by the activation energy of crystallization. Our results suggest that silicate crystallization occurs in wider astrophysical conditions than hitherto considered.