Image segmentation is a fundamental challenge in computer vision, transforming complex image representations into meaningful, analyzable components. While entropy-based multilevel thresholding techniques, including Otsu, Shannon, fuzzy, Tsallis, Renyi, and Kapur approaches, have shown potential in image segmentation, they encounter significant limitations when processing thermal images, such as poor spatial resolution, low contrast, lack of color and texture information, and susceptibility to noise and background clutter. This paper introduces a novel adaptive unsupervised entropy algorithm (A-Entropy) to enhance multilevel thresholding for thermal image segmentation. Our key contributions include (i) an image-dependent thermal enhancement technique specifically designed for thermal images to improve visibility and contrast in regions of interest, (ii) a so-called A-Entropy concept for unsupervised thermal image thresholding, and (iii) a comprehensive evaluation using the Benchmarking IR Dataset for Surveillance with Aerial Intelligence (BIRDSAI). Experimental results demonstrate the superiority of our proposal compared to other state-of-the-art methods on the BIRDSAI dataset, which comprises both real and synthetic thermal images with substantial variations in scale, contrast, background clutter, and noise. Comparative analysis indicates improved segmentation accuracy and robustness compared to traditional entropy-based methods. The framework's versatility suggests promising applications in brain tumor detection, optical character recognition, thermal energy leakage detection, and face recognition.