The emergence of biomedical sensor devices, wireless communication, and innovation in other technologies for healthcare applications result in the evolution of a new area of research that is termed as Wireless Body Area Networks (WBANs). WBAN originates from Wireless Sensor Networks (WSNs), which are used for implementing many healthcare systems integrated with networks and wireless devices to ensure remote healthcare monitoring. WBAN is a network of wearable devices implanted in or on the human body. The main aim of WBAN is to collect the human vital signs/physiological data (like ECG, body temperature, EMG, glucose level, etc.) round-the-clock from patients that demand secure, optimal and efficient routing techniques. The efficient, secure, and reliable designing of routing protocol is a difficult task in WBAN due to its diverse characteristic and restraints, such as energy consumption and temperature-rise of implanted sensors. The two significant constraints, overheating of nodes and energy efficiency must be taken into account while designing a reliable blockchain-enabled WBAN routing protocol. The purpose of this study is to achieve stability and efficiency in the routing of WBAN through managing temperature and energy limitations. Moreover, the blockchain provides security, transparency, and lightweight solution for the interoperability of physiological data with other medical personnel in the healthcare ecosystem. In this research work, the blockchain-based Adaptive Thermal-/Energy-Aware Routing (ATEAR) protocol for WBAN is proposed. Temperature rise, energy consumption, and throughput are the evaluation metrics considered to analyze the performance of ATEAR for data transmission. In contrast, transaction throughput, latency, and resource utilization are used to investigate the outcome of the blockchain system. Hyperledger Caliper, a benchmarking tool, is used to evaluate the performance of the blockchain system in terms of CPU utilization, memory, and memory utilization. The results show that by preserving residual energy and avoiding overheated nodes as forwarders, high throughput is achieved with the ultimate increase of the network lifetime. Castalia, a simulation tool, is used to evaluate the performance of the proposed protocol, and its comparison is made with Multipath Ring Routing Protocol (MRRP), thermal-aware routing algorithm (TARA), and Shortest-Hop (SHR). Evaluation results illustrate that the proposed protocol performs significantly better in balancing of temperature (to avoid damaging heat effect on the body tissues) and energy consumption (to prevent the replacement of battery and to increase the embedded sensor node life) with efficient data transmission achieving a high throughput value.