Accurate measurement of the thermal conductivity of a heat transfer fluid (HTF) is important for optimizing the performance of a thermal energy storage system. Herein, we develop a system to measure the thermal conductivity of an HTF during temperature variation, and the system was checked to measure several samples comprising water, lauric acid, stearic acid, oleic acid, and coconut oil. The thermal conductivity was measured using a KS-1 sensor of a KD2 Pro analyzer. In the study, a static heat conducting medium was used to control the temperature of the fluid, instead of the commonly used flowing water bath. The measured thermal conductivities of water (298 to 318 K) and lauric acid (323 to 373 K), stearic acid (358 to 372 K), oleic acid (334 to 372 K), and coconut oil (298 to 363 K) were compared to data from previous studies and fitted to available models. The accuracy of the data is further analyzed by relating the number of C and H atoms in the fatty acid, and the fatty acid content in coconut oil.