A thermal compressor heat pump is a thermally driven heat pump application that mainly uses thermal energy to drive a compression cycle, delivering heat to the user. The thermal energy can be in the form of waste heat, combustion of natural gas, or solar, which would contribute to the demand for higher-efficiency machines and decreasing greenhouse gas emissions. The thermal energy is directly received by the thermal compressor, which aims to convert it into compression power, replacing a conventional electric compressor. Exergy analysis is gaining more interest today as it offers a deep and detailed analysis of the inefficiencies in a system. Such analysis highlights the highest deficiencies in components and the maximum possible potential for process optimization. Being an important component, an overall performance optimization of a thermal compressor heat pump cannot bypass the optimization of its compressor. For this reason, we carry out an exergy analysis on the thermal compressor integrated into a single-stage heat pump cycle, based on previously derived data-driven models. A parametric exergy analysis is carried out to find the optimal operating conditions at the level of a thermal compressor first, and second on a single-stage thermal compressor heat pump cycle.