The hot wire method is one of the few methods that can be applied to measure the thermal conductivity of materials at 1000 °C and above. However, in the case of granular or electrically conductive materials, the heating wire and thermocouple must be insulated from the material by placing them in a sheath (or a needle). In this case, it is shown that the method of using the slope of the curve T = f[ln(t)] could lead to estimation errors of up to 30% for some materials. A complete quadrupolar model of the system needle/material is developed, and a sensitivity analysis of the probe temperature to the different parameters allowed for the selection of a reduced model, enabling a precise estimation of the thermal conductivity. Measurements carried out between 600 and 1000 °C on a material of known thermal conductivity led to deviations of less than 3%. The method is finally applied up to 1000 °C to two granular materials and to compacted molding sand with quite a good fitting between the experimental and modeled curves.