Though very promising, fatty acids suffer from low thermal conductivity and leakage, which limits their heat storage applications. To overcome these problems, we used silica fume (SF) to house the fatty acid and prevent leaching during phase change and incorporated different amount (1.0, 3.0 and 5.0 wt%) of CNTs to improve the thermal conductivity to the desired level. For the experimental temperature range and better performance an eutectic mixture of capric acid(CA)-palmitic acid(PA) was prepared and investigated. The physicochemical and morphological characterizations of the fabricated shape stabilized-composite PCMs (SS-CPCMs) with/without CNTs were carried out using FTIR, XRD and SEM instruments. The DSC analysis results showed the SS-CPCMs had phase change temperatures of 19-26 degrees C and high latent heat capacity of 46-49 J/g, which are suitable for thermal energy storage (TES) in buildings. The SS-CPCMs showed good cycling TES reliability and chemical stability and also exhibited excellent thermal durability up to 140 degrees C. The CNTs doping process caused an appreciable increase in thermal conductivity and significantly reduced the charging and discharging times of the SS-CPCMs. Consequently, due to higher thermal conductivity, the SS-CPCM doped with 5.0 wt% CNTs can be considered as more promising composite for passive solar thermoregulation of building envelopes.