Today, the study of thermal systems that take advantage of residual thermal sources in the power generation sector is of great importance to mitigate environmental impact and promote sustainable alternatives in this sector. Among these alternatives, the organic Rankine cycle (ORC) is of great relevance since it allows taking advantage of residual energy sources at low temperatures. This work presents a methodology to evaluate the feasibility of using a refrigerant as a working fluid in an organic Rankine cycle based on an exergetic viability index. As a case study, R134a, R600a, R245fa, and R123 refrigerants were considered. A residual thermal source was used that came from the Hybrid Cycle Plant of the Valley of Mexico. Thermodynamic analysis was performed to determine generated power, thermal efficiency, refrigerant mass flow, pinch point temperature difference, specific steam consumption, unused thermal exergy flow, exergy efficiency, and total heat transfer requirement. The weighted average of the differences between these indicators, the global warming index, and the ozone depletion potential relative to the most favorable indicator corresponded to the definition of the exergetic viability index of the refrigerant. The results indicate that the ORC operating at condensing temperatures of 25, 35, and 45 °C with R245fa shows the highest rate of exergetic viability despite not generating the greatest amount of power and being one of the refrigerants with the highest total heat transfer requirement. Finally, at condensing temperatures above 45 °C, it is observed that R600a is exergetically the most viable refrigerant used in the ORC.