Thermal management is a growing challenge for electronics packaging because of increased heat fluxes and device miniaturization. Thermal interface materials (TIMs) are used in electronic devices to transfer heat between two adjacent surfaces. TIMs need to exhibit high thermal conductivity and must be soft to minimize thermal contact resistance. Polymers, despite their relative softness, suffer from low thermal conductivity (∼0.2 W/m-K). To overcome this challenge, we infiltrate nanoporous anodic aluminum oxide (AAO) templates with molten polymer to fabricate large area arrays of vertically aligned polymer nanofibers. Nanoscale confinement effects and flow induced chain elongation improve polymer chain alignment (measured using polarized Raman spectroscopy) and thermal conductivity (measured using the photoacoustic method) along the fiber’s long axis. Conjugated poly(3-hexylthiophene-2,5-diyl) (P3HT) and non- conjugated polyethylene (PE) of various molecular weights are explored to establish a relationship between polymer structure, nanofiber diameter, and the resulting thermal conductivity. In general, thermal conductivity improves with decreasing fiber diameter and increasing polymer molecular weight. Thermal conductivity of approximately 7 W/m-K was achieved for both the ∼200 nm diameter HDPE fibers and the 100 nm diameter P3HT fibers. These results pave the way for optimization of the processing conditions to produce high thermal conductivity fiber arrays using different polymers, which could potentially be used in thermal interface applications.