Out-of-order (OoO) processors generally offer significant performance gains over simpler in-order (InO) processors. However, recent studies have revealed that OoO processors provide little performance benefit in many program phases, and these phases are distributed in fine granularity. Leveraging these fine-grained phases, tightly coupled heterogeneous cores (TCHCs) have been proposed to improve the energy efficiency. A TCHC, which is a processor core that consists of multiple back-ends, each with different characteristics in terms of their performance and energy consumption (e.g., a power-efficient InO back-end and a high-performance OoO back-end), improves the energy efficiency by executing programs by switching to the most energy-efficient back-end with a very small switching penalty. We propose a novel technique to further improve the energy efficiency of a TCHC. The proposed technique is based on runahead execution (RAE), which is a prefetch technique that executes instructions ahead of long-latency cache misses and issues independent cache misses earlier. Leveraging the characteristics of TCHCs and RAE, the proposed technique increases the utilization of energy-efficient back-ends, thereby significantly improving the energy efficiency. Our evaluation results show that our proposed method achieves 13% of energy-delay product (EDP) over a state-of-the-art TCHC using Oracle switching decision logic.