The demand for wearable electronics has resulted in an increasing interest in the development of functional fibers, with a specific focus upon the development of electrically conductive fibers incorporable into garments. However, the production of thermally conductive fibers for heat dissipation has been largely neglected. Owing to the very rapid development of miniaturized wearable electronics, there is an increasing need for the development of thermally conductive fibers as heat sinks and thermal management processes. In this study, thermally conductive but electrically insulating boron nitride nanopowder (BNNP) fillers are used to effectively enhance the thermal conductivity and mechanical properties of elastomeric polyurethane fibers. Thermal conductivity enhancement of more than 160% is achieved at very low loadings of BNNP (less than 5 wt%) with an improvement in the mechanical properties of the unmodified fiber. These thermally conductive fibers are also incorporated into 3D textile structures as a proof of processability.