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Customized engineered fibers are currently being used extensively in the aerospace and automobile industries due to the ability to “design in” specific engineering characteristics. Understanding the thermal conductivity of these new fibers is critical for thermal management and design optimization. In the current investigation, a steady-state dc thermal bridge method (DCTBM) is developed to measure the thermal conductivity of individual poly(ether ketone) (PEK)/carbon nanotube (CNT) fibers. For non-conductive fibers, a thin platinum layer was deposited on the test articles to serve as the heater and temperature sensor. The effect of the platinum layer on the thermal conductivity is presented and discussed. DCTBM is first validated using gold and platinum wires (25 μm in diameter) over a temperature ranging from room temperature to 400 K with ±11% uncertainty, and then applied to PEK/CNT fibers with diverse CNT loadings. At a 28 wt. % CNT loading, the thermal conductivity of fibers at 390 K is over 27 Wm-1K-1, which is comparable to some engineering alloys.