Infrared thermography (IRT) is gaining momentum in sports medicine as a non-invasive technique for early injury detection and physiological monitoring. In this study, the authors present a novel computational thermography framework that leverages high-dimensional (HD) thermomic feature extraction and nonlinear dimensionality reduction for the temporal analysis of thermal responses associated with physical activity. Thermal data were collected from 12 rugby players under standardized conditions at three key timepoints: pre-exercise, immediately post-exercise, and post-rest. A fixed region of interest (ROI) over each knee was analyzed to assess localized thermal changes. We employed PR-Isomap for HD-to-low-dimensional (LD) thermomics distillation and introduced a κ-embedding strategy to integrate temporal data. Statistical analyses using the Wilcoxon test revealed significant differences in thermal patterns across timepoints, with 213, 179, and 89 significantly altered LD attributes for Before/During, During/After, and Before/After comparisons, respectively. Despite the limited sample size, the unsupervised model achieved a predictive accuracy of 66.7%, identifying early signs of tissue stress with minimal misclassification. These findings validate the feasibility of our method and highlight its potential application in real-time, personalized injury risk assessment and athlete monitoring. The integration of statistical inference and machine learning with IRT paves the way for scalable, interpretable, and non-invasive approaches to sports injury prevention and performance optimization.