Energy storage is an effective approach to bridging the gap between energy supply and demand created due to the sporadic nature of solar energy. Thermal performance enhancement is a key research subject for effective energy storage using latent heat thermal energy storage (LHTES) systems. This paper focuses on the analysis-based design of suitable LHTES system components for solar absorption-based cooling applications with a working temperature of up to 200 °C. Initially, the medium-temperature range (80 °C to 200 °C) phase change material (PCM) is selected using the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS). Further, a suitable heat transfer fluid (HTF) is selected along with the design of a geometrical assessment and an appropriate LHTES system. Finally, the effect of the stirrer on the thermal performance of the LHTES system has been discussed. The melting time of PCM reduces by 58% while input energy increases by 20 kJ with an increase in HTF inlet temperature from 180 °C to 190 °C. However, input energy increases faster with a further increase in HTF inlet temperature while melt time does not reduce significantly. Therefore, selecting optimum HTF inlet temperature is an important criterion for efficient LHTES system design. Implanting a rotating stirrer at 200 RPM inside a PCM tube decreases the net-input energy by 73 kJ. Using back-of-the-envelope calculations, the analysis-based selection of key components of the LHTES system will pave the way forward to designing an application-specific LHTES system. Further, this study can be instrumental in theoretically scrutinizing the stirring effect on PCM charging before experimental analysis.