A new method is proposed to measure the longitudinal thermal conductivity of fibers and films. The thermal conductivity of novel one- and two-dimensional materials has previously been measured using a T-type probe. Although this method is applicable to polymer fibers and films, the measurements are influenced by the thermal contact resistance between the probe and the sample. We therefore propose a so-called ITX method, which determines the inherent thermal conductivity of a sample from measurements made in three geometric configurations (“I”, “T”, and “X” shape) of the sample, heat sinks, and measurement probe. Application of the method to DNA solid films demonstrated that the thermal conductivity can be accurately determined irrespective of the relative contribution of the thermal contact resistance to the overall thermal resistance.