The transient hot-wire (THW) technique is an absolute technique for measuring the thermal conductivity of fluids. In this work, a THW apparatus was developed for measurements over the temperature range from 193 to 424 K at pressures up to 34 MPa. The apparatus was commissioned with the measurements of pure argon, methane, and propane along several isotherms at pressures up to 33 MPa. The measured values agreed with those calculated with the reference equations within the uncertainty of the equations. Thermal conductivity measurements of a binary mixture (0.9514 methane + 0.0486 propane) were then carried out in the temperature range from 195 to 424 K at pressures up to 31 MPa in a single phase and near the bubble point curve. The relative combined expanded uncertainties (k = 2) for these single-phase and bubble-point mixture measurements were estimated as 2.0 and 5.0%, respectively. The relative deviations of these measured values from those calculated with the extended corresponding state model implemented in the software package REFPROP 10.0 were within 4.4 and 8.0%, respectively.