Dermatological diseases are commonly diagnosed through visual examination which may be influenced by lesion appearance imaging conditions and clinical experience. Infrared thermal imaging offers a non-contact and radiation-free approach for capturing physiological changes associated with inflammation blood perfusion and metabolic activity. This paper presents a preliminary exploratory statistical investigation of infrared thermal signatures for characterizing dermatological disease using Gaussian Mixture Modelling (GMM) conducted on a small pilot cohort of two acne-affected and two healthy subjects. Thermal images were analysed through channel-wise decomposition of the red (R) green (G) and blue (B) colour channels and for each channel a four-component GMM was fitted to model the intensity distribution from which statistical descriptors mean standard deviation variance skewness and kurtosis were extracted. Given the limited sample size no inferential statistical testing was performed; the analysis is descriptive and exploratory in nature. Within this pilot dataset diseased subjects showed higher R-channel intensity lower B-channel intensity and greater thermal heterogeneity than healthy subjects while the G-channel showed comparatively limited separation between groups. The probabilistic representation provided by GMM captured the heterogeneous thermal patterns observed in the diseased samples. These preliminary observations while not statistically generalizable due to the small and anatomically unmatched cohort suggest that channel-wise statistical analysis of infrared thermal images may reveal interpretable thermal signatures worth investigating further. The proposed framework is intended as an early step toward a statistical foundation for future machine learning and deep learning studies using larger anatomically matched dermatological thermal image datasets.