Liquid crystal elastomers (LCEs), consisting of polymer networks and liquid crystal mesogens, show a reversible phase change under thermal stimuli. However, the kinetic performance is limited by the inherently low thermal conductivity of the polymers. Transforming amorphous bulk into a fiber enhances thermal conductivity through the alignment of polymer chains. Challenges are present due to their rigid networks, while cross-links are crucial for deformation. Here, we employ hydrodynamic alignment to orient the LCE domains assisted by controlled in situ cross-linking and to remarkably reduce the diameter to submicrons. We report that the intrinsic thermal conductivity of LCE fibers at room temperature reaches 1.44 ± 0.32 W/m-K with the sub-100 nm diameter close to the upper limit determined in the quasi-1D regime. Combining the outstanding thermal conductivity and thin diameters, we anticipate these fibers to exhibit a rapid response and high force output in thermomechanical systems. The fabrication method is expected to apply to other cross-linked polymers.