Widespread utilization of geothermal energy as a clean energy source can reduce the use of fossil fuels and thereby protect the environment. Previous combined heat and power (CHP) systems using low-temperature geothermal heat as a heat source have limited utilization of geothermal heat. In this study, a cogeneration system based on organic Rankine cycle (ORC) and absorption heat exchanger (AHE) is designed. We analyzed the thermal efficiency, exergy efficiency, and economics of the proposed system utilizing 85 °C low-temperature geothermal heat, and the optimal operating fluid for this system is discussed. The results show that the optimal working fluid for the proposed system is R245fa. Using R245fa as the working fluid, the proposed system can achieve an exergy efficiency of 61.39%, when the heat source outlet temperature can be as low as 23 °C, while the proposed system can achieve the lowest LCOE of 0.082 ($/kW ·h) when using R22 as the working fluid.