The aim of the study was to develop predictive models of thiol group (SH) level changes in minced raw and heat-treated chicken meat enriched with selected plant extracts (allspice, basil, bay leaf, black seed, cardamom, caraway, cloves, garlic, nutmeg, onion, oregano, rosemary, and thyme) during storage at different temperatures. Meat samples with extract addition were stored under various temperatures (4, 8, 12, 16, and 20 °C). SH changes were measured spectrophotometrically using Ellman’s reagent. Samples stored at 12 °C were used as the external validation dataset. SH content decreased with storage time and temperature. The dependence of SH changes on temperature was adequately modeled by the Arrhenius equation with average high R2 coefficients for raw meat (R2 = 0.951) and heat-treated meat (R2 = 0.968). Kinetic models and artificial neural networks (ANNs) were used to build the predictive models of thiol group decay during meat storage. The obtained results demonstrate that both kinetic Arrhenius (R2 = 0.853 and 0.872 for raw and cooked meat, respectively) and ANN (R2 = 0.803) models can predict thiol group changes in raw and cooked ground chicken meat during storage.