Technological progress is needed to develop renewable energies. Improvements should be especially focused on the energy storage element to help correct the mismatch between energy supply and demand. In concentrated solar power (CSP) plants, ordinary concrete made of Portland cement (PC) has been proven to be a good thermal energy storage (TES) medium. However, the substantial environmental impact of PC manufacturing makes it necessary to develop new materials. Thus, in this work, alternative alkali-activated mortars (AAM) and hybrid materials (HM) have been developed using blast furnace slag to replace PC. This has been done in order to study their stability at high temperature (up to 500 °C) and their viability to operate as TES, undergoing thermal cycles between 200 °C and 400 °C, as they would in CSP technologies. Studying the mechanical and thermal properties after the thermal treatments has revealed that the alternative materials offer improved mechanical properties as well as very good thermal conductivity and storage capacity values. In particular, the best results in terms of mechanical properties were achieved by the AAM system, where the compressive strength value is increased with respect to the reference PC sample by 195% after exposure to 500 °C and by almost 97% after 20 thermal cycles between 200 °C and 400 °C. Furthermore, in terms of thermal properties, the AAM system showed a 31% increase in thermal conductivity after thermal exposure compared to PC. In addition, both AAM and HM systems demonstrated substantial improvements in specific heat and thermal storage capacity, outperforming PC by up to 46% during CSP-like thermal cycles. These promising results open new doors to the study of these alternative materials, such as TES, as they are more suitable than PC from an operational point of view.