Infrared thermography has been used as a key means for the identification of overheating defects in power cable accessories. At present, analysis of thermal imaging pictures relies on human visual inspections, which is time-consuming and laborious and requires engineering expertise. In order to realize intelligent, autonomous recognition of infrared images taken from electrical equipment, previous studies reported preliminary work in preprocessing of infrared images and in the extraction of key feature parameters, which were then used to train neural networks. However, the key features required manual selection, and previous reports showed no practical implementations. In this contribution, an autonomous diagnosis method, which is based on the Faster RCNN network and the Mean-Shift algorithm, is proposed. Firstly, the Faster RCNN network is trained to implement the autonomous identification and positioning of the objects to be diagnosed in the infrared images. Then, the Mean-Shift algorithm is used for image segmentation to extract the area of overheating. Next, the parameters determining the temperature of the overheating parts of cable accessories are calculated, based on which the diagnosis are then made by following the relevant cable condition assessment criteria. Case studies are carried out in the paper, and results show that the cable accessories and their overheating regions can be located and assessed at different camera angles and under various background conditions via the autonomous processing and diagnosis methods proposed in the paper.