Incorporating phase change capsules into polymeric matrices is an effective approach for developing flexible composites with both heat storage capacity and good thermal reliability, while the interfacial heat conductance between the capsules and the matrix has seldom been considered. Herein, paraffin@SiO2 nanocapsules synthesized by an interfacial polycondensation process using a basic catalyst were incorporated into a polydimethylsiloxane matrix for the first time to prepare phase change composites at different loadings. Furthermore, the composites containing the nanocapsules were systematically compared with the composites containing the paraffin@SiO2 microcapsules synthesized using an acidic catalyst. It is shown that, at every identical mass fraction, the composites containing the nanocapsules not only possessed larger latent heat than those containing the microcapsules, but also exhibited higher thermal conductivity and lower hardness. The enhancement in thermal conductivity as well as the decline in hardness for the composite containing the nanocapsules are revealed to originate from a larger amount of hydroxyl groups at the surfaces of the nanocapsules than the microcapsules, which could form more hydrogen bonds with the polymer matrix. This bonding favored the interfacial heat conductance between the nanocapsules and the matrix together with decreasing the crosslinking density of the matrix. Subsequently, composites with enhanced thermal conductivity were developed by combining the nanocapsules with a BN filler. By evaluating the performance for chip heat dissipation, it was found that, when the chip was heated at a power of 10 W, the incorporation of the paraffin@SiO2 nanocapsules at a loading of 36 wt% into the polymer matrix made a remarkable decrease in the chip equilibrium temperature by 31.7 °C, and a further decline by 8.9 °C occurred when combined with 16 wt% BN. This work sheds light on facilitating the interfacial heat conductance between phase change capsules and the polymer matrix by hydrogen bonding.