Thermoelectric oxide nanofibers prepared by electrospinning are expected to have reduced thermal conductivity when compared to bulk samples. Measurements of nanofibers’ thermal conductivity is challenging since it involves sophisticated sample preparation methods. In this work, we present a novel method suitable for measurements of thermal conductivity in a single nanofiber. A microelectro-mechanical (MEMS) device has been designed and fabricated to perform thermal conductivity measurements on a single nanofiber. A special Si template was designed to collect and transfer individual nanofibers onto a MEMS device. Pt was deposited by Focused Ion Beam to reduce the effective length of a prepared nanofiber. A single La0.95Sr0.05CoO3 nanofiber with a diameter of 140 nm was studied and characterized using this approach. Measured thermal conductivity of a nanofiber was determined to be 0.7 W/m•K, which is 23% of the value reported for bulk La0.95Sr0.05CoO3 samples.