The problems of low-contrast, blurred images, and low-edge details are encountered in infrared images. These undesirable features affect infrared imaging applications in military, science, medicine, and other fields. Therefore, a method of edge detection based on heat conduction matrix (HCM) has been proposed to show or sharpen the edges of objects in infrared images. First, the heat conduction formula of solid and still fluids was applied on the infrared image, and a feature matrix called HCM was obtained. Second, the HCM feature matrix was passed through a threshold to obtain distinct and noise-free edge images. The results of the numerical and visual applications were compared with the Sobel, Canny, and Laplacian of Gaussian methods. The results of our study showed that the proposed method is powerful in detecting edges in infrared images. The most important feature of the method is its high emphasis on important edges as well as thin and distinct edges.