Molecularly confined polymer fillers in nanopores were found to give superior mechanical properties of polymer nanocomposites. In this work, we study the thermal conductivity of such nanocomposites and unveil the effect of polymer confinement on thermal conductivity. Using the time-domain thermoreflectance method, we measure the cross-plane thermal conductivity of polymer nanocomposites that consist of polystyrene fillers confined within a nanoporous organosilicate matrix. Compared to unconfined bulk polystyrene fillers, we find that pore-confined polystyrene fillers enhance the thermal conductivity of the polymer nanocomposites. This enhancement is attributed to the better aligned and less entangled chains in the confined phase, where chain-chain phonon scatterings are reduced. Our work provides essential insights into the thermal conductivity of polymer nanocomposites for multifunctional thermal and mechanical applications.