The performance of the commonly-used transient hot wire technique for measuring the thermal conductivity of materials near their liquid-solid transition point is reported in this paper. Adopting a 1-D transient formulation, the computational methodology is discussed in detail and predictions of the wire temperature are compared to the limiting analytical solutions without and with phase change. By varying the initial solid-state temperature of an eicosane sample, six cases which undergo phase change to different extent were studied. The results exhibit a monotonic dependence of the predicted thermal conductivity value on the initial temperature of the solid medium. As the initial temperature of the solid-state sample approaches the melting point, the predicted thermal conductivity value moves toward the value of the liquid eicosane. Recommendations were provided for performing measurements of thermal conductivity using the transient how wire technique involving phase change. (C) 2017 Elsevier Ltd. All rights reserved.