The growth of the world's population, especially that of the elderly, along with the outbreak of infectious diseases such as COVID-19 have caused hospitals and healthcare centres to become full, and even economical treatments cost a lot. On that account, the conjunction of wireless body area networks (WBAN) and Internet of Things (IoT) for healthcare and medical diagnosis has become really important, and is accordingly one of the most popular and attractive areas of the Internet of Things (IoT). In such an IoT, a wireless body area network (WBAN) consists of a miniature sample of the Internet of Medical Things (IoMT) that can be either implanted in the human body or wearable. Nowadays, IoT has made healthcare evaluation possible. Instead of the patient being constantly hospitalized for treatment, the condition of the person is sent to the health centre by the IoMT over the Internet. IoT enables wireless communication between smart devices on one side and almost anything on the other. Since this network deals with medical and critical conditions, data must be sent to a physician or practitioner in the prescribed period; this indicates that routing is one of the most critical issues. Thus, routing is considered a very important challenge in WBANs. The present study describes thermal (temperature)-aware routing protocols in WBANs. Routing protocols in WBANs are divided into thermal (temperature)-aware, QoS-aware, security-aware, cluster-based, cross-layered, postured-based, cost-effect, link-aware, and opportunistic ones. In a WBAN, temperature rise in implant nodes can damage body tissues, which is dangerous for the patient. Accordingly, here, those algorithms were considered which are presented in thermal (temperature)-aware protocols. This paper first introduces IoT-based WBANs, their routing mechanism and challenges, after which it provides a detailed description of thermal (temperature)-aware algorithms. Finally, the advantages and disadvantages of these algorithms are presented.