Phase change materials (PCMs) are considered to be promising contenders for thermal energy storage (TES) due to their high latent heat and nearly constant temperature during the intake/release of heat. The present study focuses on providing the most suitable PCM for low-temperature (40–80 °C) heat storage applications. However, the selection of the most suitable one from the wide range of PCMs for an application needs a thorough insight of their thermophysical properties, thermal stability, compatibility, and melting and solidification behavior. Among the PCMs available for low-temperature heat storage applications, organic PCMs stand as an attractive option. Based on melting point temperature, latent heat, cost, and ease of availability, five widely used organic PCMs, viz., lauric acid (LA), myristic acid (MA), stearic acid (SA), paraffin wax (PW), and palmitic acid (PA), are selected. Initially, thermophysical properties are measured and tabulated. Subsequently, thermal stability experiments up to 1500 melting/freezing cycles, compatibility studies with container materials (aluminum and stainless steel (SS)), and melting and solidification experiments giving total melting and solidification times are performed. Further, a hybrid multiple attribute decision-making (MADM) method is employed to select the best PCM based on the obtained experimental results. During the selection process at first, the subjective weights of the attributes are measured according to the analytical hierarchy process (AHP). Later, the PCMs are ranked based on the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). The hybrid MADM results show that among the selected PCMs, paraffin wax is the optimal PCM for low-temperature heat storage applications.