Inexpensive site-independent electricity storage is widely believed to be the solution to the global problem of economically storing large amounts of electricity generated from renewable energy sources. In particular, high exergy densities, scalability, long duration, and small environmental impact are desired. Thermal exergy storages (TEXS) is a new term introduced here for the characterization of energy storage systems, in which electricity is stored in the form of thermal exergy in low-cost storage media. A large number of TEXS concepts exist under various names. In this paper, a preliminary classification is elaborated. Parameters of importance to these properties are identified and varied in a sensitivity analysis. Potential key performance indicators, challenges, and limitations of the technologies are conducted from the analysis. Four TEXS systems are simulated and further evaluated with exergy-based methods: two Brayton-based pumped thermal ES systems with solid and liquid storage materials, one liquid air energy storage system, and one Lamm-Honigmann energy storage system were studied. The systems are simulated using the software AspenPlus, Modelica, Matlab, and EbsilonProfessional. The exergy density and the separate consideration of the exergetic efficiencies of the charging and discharging process were shown to be valuable for a comprehensive comparison. The sensitivity of the identified key performance indicators gave a first impression on the performance of the systems during part-load operation. An economic assessment of the proposed systems was is crucial for further assessment. The analyses and comparisons of different TEXS concepts facilitate the further development and commercialization of low-cost, large-scale electricity storage technologies.