A relative transient hot-wire apparatus for the measurement of the thermal conductivity of electrically conducting liquids is described. The instrument consists of a single glass capillary filled with mercury to act as an insulated hot wire. The resistance change in the wire with respect to time is used to obtain the thermal conductivity of the liquid surrounding the wire with an estimated accuracy of ±2%. The most significant advantage of the liquid metal filled glass capillary is its increased temperature limit compared to other types of transient hot-wire cells. The use of the new method at temperatures up to 493 K is shown for several aqueous systems, and new data are reported for propionic acid + water mixtures.