Thermal conductivity is an essential property to understand the rate of charging/discharging of thermal energy storage systems, but there is still a lack of experimental studies in this field. The temperature dependence of thermal conductivity of eutectic mixtures capric/myristic acid (CA/MA), lauric/myristic acid (LA/MA), and palmitic/stearic acid (PA/SA), as well as their respective shape-stabilized forms (SS-PCMs), were measured by the hot wire technique. Thermal conductivity presented a linear correlation with temperature for all the materials. Besides, the thermal conductivity of the samples was compared with a commercial SS-PCM finding out that the SS-PCMs produced by the authors exhibit higher thermal conductivity than the commercial sample, with an increase between 10.57% and 33.33%. In addition, the minerals that comprise the clay were acquired and their effect on the thermal conductivity on the support studied. Between the crystalline phases, kaolin governed the thermal conductivity of the support. Afterward, kaolin additions were made, resulting in an increase of thermal conductivity between 6.49% and 17.68% of the SS-PCM. Thus, the novelty of this study relies, first, on the experimental data obtained of thermal conductivity, and second, on the study of the effect of some minerals in the overall thermal conductivity of the samples.