Crystalline polymers have attracted significant interest in recent years due to their enhanced mechanical and thermal properties. As one type of organic-inorganic hybrid polymer crystals, polysilsesquioxane can be synthesized by large-scale and inexpensive so-gel processes with two precursors. In this paper, both octylene-bridged and hexylene-bridged PSQ crystals are characterized with infrared spectroscopy and X-ray crystallography to reveal their super high crystallinity. To study the thermal transport in these unique polymer crystals, we use a suspended micro thermal device to examine their thermal properties from 20 K to 320 K, and demonstrate their tunable thermal conductivity by varying the length of alkyl chains. We also conduct non-equilibrium molecular dynamics simulations to study the phonon behaviors across the hydrogen bond interface. The simulation results demonstrate good agreement with the experimental results regarding both the value and trend of the PSQ thermal conductivity. Furthermore, from the simulation, we find that the anharmonic phonon scattering and interfacial anharmnic coupling effects across the hydrogen bond interface may explain the experimentally observed thermal properties.