The capric acid (CA)/diatomite (DT)/carbon nanotube (CNT) ternary system was investigated to develop a shape-stabilized composite phase change material for thermal energy storage via the direct impregnation method. DT was used as the supporting material to absorb CA and prevent its leakage. It was found that good form stability could be obtained when the loading of capric acid in the CA/DT composite reached about 54%. Furthermore, CNTs were added into the CA/DT form-stable phase change material (FSPCM) to enhance the thermal conductivity of the binary system. Moreover, the X-ray diffraction, scanning electron microscopy, and Fourier transform infrared spectroscopy analyses were carried out to characterize the microstructure and chemical properties of the composite PCM. The thermal properties of the prepared form-stable phase change materials (FSPCMs) were determined using differential scanning calorimetry (DSC) and thermogravimetric analyses. The analysis results showed that the components of the FSPCMs were in good compatibility and CA is well-infiltrated into the structure of the DT/CNT matrix. DSC analysis indicated that the latent heat of fusion of the ternary system was 79.09 J g^–1 with a peak melting temperature of 31.38 °C. The thermal conductivity of the CA/DT/CNTs increased from 0.15 to 0.48 W m^–1 K^–1, with only 7 wt % of CNTs. It is shown that the thermal conductivity of the ternary system was greatly enhanced by the addition of CNTs. The thermal conductivity increased by 1.56 times compared to that of the binary system. Moreover, the enhancing mechanisms of heat conduction transfer by CNTs were revealed by taking advantage of energy wave theory.