With the rapid development of renewable energy technologies, the exploitation of geothermal energy has become a vital part of future sustainable energy supply. This paper introduces and validates the feasibility of a novel geothermal energy extraction method that obtains geothermal energy by cyclically storing fluid in underground hydraulic fracture for heat exchange using only a single well. Compared to traditional enhanced geothermal system (EGS) methods, this new approach offers superior efficiency and sustainability, and does not have the risk of thermal breakthrough. We developed mathematic models that couples rock fracture mechanics and heat transfer to simulate geothermal energy extraction. Our study analyzed the variations in temperature and energy under long-term geothermal production conditions, as well as the factors influencing these changes. This study also provides a theoretical basis for the optimization design of single-well geothermal extraction via cyclic injection and flow-back.