Thermal energy storage (TES) systems can be used for recovering industrial waste heat and increasing energy efficiency, especially when coupled to batch thermal processes. Stratified water thermal storage tanks are the preferred technology for low-temperature applications, while molten salts are commonly used in medium and high-temperature applications with large storage capacities. No clear consensus exists on the appropriate TES technology for different industrial demands characteristics and their respective heat supply systems for medium and high-temperature applications. The present study analyzes several industrial sectors and their thermal processes, analyzing their temperature ranges, heat demands, and available TES technologies, which are classified by their operational conditions. The study presents two novel indicators for a preliminar compatibility assessment between TES and industrial sectors: a temperature compatibility indicator and exergy efficiency for TES and thermal processes. The results show that low and medium-temperature applications such as food, chemical, or textile industries exhibit high compatibilities with water (over 64%), high-temperature PCM (over 61%), and solid-state TES (100%), whereas molten salts and chemical looping demonstrate lower compatibility (below 24%). The exergy analysis for industrial cases shows that a lower temperature operating range for a TES induces low exergy efficiency. Regarding this scenario, high-temperature cPCM reaches efficiencies of over 44% for mid and high-temperature processes. Conversely, solid-state TES emerges as the most viable option for integration in high-temperature industries, exhibiting an efficiency of 62% with minimal exergy losses. The indicators defined in this study can be used for an early evaluation of TES integration in industrial applications, thus promoting emerging technologies selection through a quantitative comparison of the compatibility metrics.