In measuring thermal conductivities of liquids by a transient line source technique, one of the main error factors involved is the owing to the heat flow from the hot wire to the electrode through the wire edge. In this report, analytical investigation is performed concerning the edge effect on the measured thermal conductivity considering two basic cases; in the first case, a hot wire is directly connected to the electrode; and in the second case, a ringwise projection having a square cross section is attached at the connection of the hot wire to the electrode. Then the effectiveness, using a Wheatstone bridge circuit where two hot wires of different lengths are set to cancel and minimize the edge effects, is discussed analytically. As a result, the edge effect cannot be negligible even when using the bridge circuit, depending on the size of projection.