Local approaches (LA) to cleavage fracture incorporate microstructure information and failure mechanisms into mathematical models for calculation of component failure probability. They offer a promising mechanistic alternative to global approaches and have been successfully applied to predict cleavage fracture toughness (CFT) changes due to material degradation and geometry effects. Predicting the dependence of CFT on temperature, specifically in the ductile-to-brittle transition (DBT) regime, remains a challenge. This work offers one avenue for addressing the challenge by revisiting the mathematical basis of LA and demonstrating that changes in continuum mechanical fields due to changes of deformation properties with temperature are insufficient to deliver predictions in agreement with experimentally measured CFT dependence on temperature. This suggests that the process by which cleavage initiators are generated is dependent on temperature separately from the dependence of the deformation properties on temperature. The temperature dependence of the generation process is derived for the material studied in the work. A methodology is described for predicting CFT in the DBT regime, using deformation and fracture toughness properties at one temperature and deformation properties at any other temperature of interest.