The emergence of the Heterogeneous Wireless Sensor Network (HWSN) has attracted the attention of researchers in recent years. In HWSN, the sensor nodes have different sensing, processing, storage, power, and communication capabilities. Different protocols, algorithms, and applications have been proposed for HWSN. However, several research challenges, for example, efficient utilization of node energy, transmission control, enhancing network lifetime, optimum route selection, and minimizing the delay involved in processing still need to be addressed. The sensor nodes are battery-powered and in most cases, it is impossible to replace the batteries. Hence, it is important to design energy-efficient solutions for HWSN. To improve energy efficiency and increase the lifetime of HWSN, we proposed a fog-based energy-efficient solution called FEDR. The design of FEDR is based on the Dijkstra algorithm. The proposed architecture was implemented in a simulation environment. We performed several experiments to evaluate the performance of FEDR. We also compare the results in terms of alive nodes and energy utilization with two state-of-the-art solutions called ACO-based routing of fog nodes (FEAR) and Pegasis-based Routing of Fog Nodes (FECR). Experimental results showed that FEDR outperforms FEAR and FECR. From the results, we conclude that our proposed solution improves the energy efficiency and lifetime of HWSN.