This research solves the “black box” problem of AI implementation in imaging by introducing a transparent, statistically grounded approach to breast cancer risk stratification via infrared thermography without compromising performance. Using the public DMR-IR dataset, statistical feature engineering was applied to training data by extracting first- and second-order statistical features. After ensuring non-normality with a Shapiro-Wilk test, feature significance was established with the Mann-Whitney U test. LASSO regularization selected the five most predictive features: mean, standard deviation, kurtosis, correlation, and energy. To counteract class imbalance, SMOTE was applied, and two machine learning models—logistic regression and random forest (classifier)—were trained on the balanced data and then evaluated on an unseen test dataset. Reporting an AUC of 0.98 over logistic regression’s 0.96 reflects stringent statistical feature engineering and great generalization, creating a strong and interpretable model for breast cancer diagnosis in thermal images, and instills more clinical confidence in AI-based diagnostic systems.