The work aims to explore the effects of boron nitride (BN) on the shape stability and thermal conductivity of lauric acid (LA), myristic acid (MA), palmitic acid (PA) and stearic acid (SA). Four different molding phase change composites were prepared by blending FA with BN after melting. The effects of BN addition, photothermal conversion, heat storage time and temperature on the density and shape stability of phase change composites, as well as the effects of BN addition on the thermal conductivity of FA phase change materials were analyzed. The results showed that the density of phase change composites increased linearly with the increase of BN content, and its stability also increased. The optimal mass fractions of BN added in the four FAs were 68%, 69%, 69% and 68%, respectively. The leakage rate of phase change composites increased linearly with the increase of heat storage time. The leakage rate was less than 0.6% after 12 h of heat storage. The leakage rate increased with the increase of heat storage temperature, and the leakage rate was less than 0.1% after heating for 3 h above the melting point of 25 °C. After four photothermal conversions, the leakage rate was less than 0.4%; the thermal conductivity of the composites was 401.91%, 597.92%, 353.74% and 304.95% higher than that of pure FA, respectively. The prepared phase change composites have different energy storage temperature, thermal conductivity and stability, which can be used as insulation materials during transportation.