Based on sodium sulfate decahydrate (SSD) and disodium hydrogen phosphate (DHPD) as binary eutectic components, the composite eutectic phase change materials (SD) were prepared by physical blending with the addition of bacterial cellulose (BC) and nucleating agent (borax and sodium thiosulfate pentahydrate). After that boron nitride (BN) was introduced to prepare composite eutectic phase change materials with enhanced thermal conductivity. The effect of m(SSD)∶m(DHPD) on the physical properties of SD were investigated based on the measurement of phase change temperature and latent heat, and the optimal ratio was selected. The effect of BN on heat transfer and cyclic stability of thermally conductive composite eutectic phase change materials were evaluated through characterizations with subcooling, phase separation, thermal conductivity and thermal cycling tests. The resulting thermally conductive composite eutectic phase change materials were applied to thermal management of model buildings to evaluate their thermal management capability. The results showed that the supercooling degree of SD was reduced to 3.4 °C after adding a mass fraction of 3% nucleating agents (percentage of the total mass of SSD and DHPD, the same below). The phase separation phenomenon of SD was eliminated after adding BC with a mass fraction of 0.5%. Effective control of the phase change temperature between 31 and 38 °C was achieved for the prepared SD. When adding a mass fraction of 5% BN (mass percentage of SD64, the same below), the thermal conductivity of composite eutectic phase change materials 5BN-SD64 increased from 0.81 of SD64 to 1.20 W/(m·K), and their phase change latent heat decreased from 205.3 J/g of SD64 to 199.6 J/g, while maintaining a phase change temperature of 31.2 °C. Moreover, the latent heat retention rate of the 5BN-SD64 was more than 93% after 50 thermal cycles. The 5BN-SD64 was used for the thermal management application of model buildings, reducing indoor temperature fluctuation of 5.6 °C.