According to the World Health Organization (WHO), Diabetes Mellitus (DM) is one of the most prevalent diseases in the world. It is also associated with a high mortality index. Diabetic foot is one of its main complications, and it comprises the development of plantar ulcers that could result in an amputation. Several works report that thermography is useful to detect changes in the plantar temperature, which could give rise to a higher risk of ulceration. However, the plantar temperature distribution does not follow a particular pattern in diabetic patients, thereby making it difficult to measure the changes. Thus, there is an interest in improving the success of the analysis and classification methods that help to detect abnormal changes in the plantar temperature. All this leads to the use of computer-aided systems, such as those involved in artificial intelligence (AI), which operate with highly complex data structures. This paper compares machine learning-based techniques with Deep Learning (DL) structures. We tested common structures in the mode of transfer learning, including AlexNet and GoogleNet. Moreover, we designed a new DL-structure, which is trained from scratch and is able to reach higher values in terms of accuracy and other quality measures. The main goal of this work is to analyze the use of AI and DL for the classification of diabetic foot thermograms, highlighting their advantages and limitations. To the best of our knowledge, this is the first proposal of DL networks applied to the classification of diabetic foot thermograms. The experiments are conducted over thermograms of DM and control groups. After that, a multi-level classification is performed based on a previously reported thermal change index. The high accuracy obtained shows the usefulness of AI and DL as auxiliary tools to aid during the medical diagnosis.