The 3ω method for thermal conductivity measurement has emerged as an effective technique applicable to micro/nanowires and thin films. This paper describes the adaptation of the method to temperatures as high as 725 K enabling reliable thermal conductivity measurements on such samples for which previously published methods have been found inadequate. In the technique, a sample wire is heated by applying a sinusoidal current at an angular frequency ω, which causes a temperature and resistance variation at an angular frequency, 2ω, leading to a voltage signal at 3ω. The sample is connected as a four-terminal resistor to a digital lock-in amplifier, which is used to detect the in-phase and out-of-phase 3ω voltages resulting from the applied 1ω current. The data are fitted by varying the values of the thermal resistance and diffusion time, both of which are functions of thermal conductivity. Measurements are made at steady state temperatures between 300 and 725 K. Meaningful measurements at elevated temperatures require that thermal losses be understood and minimized. Conduction losses are prevented by suspending the sample above the mounting substrate. Convection losses are minimized by maintaining a vacuum of ~10(-5) torr inside the sample chamber. To minimize radiation losses, an appropriately sized sample is shrouded with a double heat-shield, with the inner shield temperature near that of the sample. Using the 3ω method, the thermal conductivity of platinum was determined to vary between 71.8 and 80.7 Wm(-1) K(-1) over the temperature range of 300 to 725 K, in agreement with published values measured for bulk samples.