A large time asymptotic solution for an unsteady heat conduction problem of a coated hot wire thermal conductivity measurement process was theoretically found. The solution revealed that the slope of wire temperature versus logarthmic time, which is used to evaluate the thermal conductivity, remains unchanged for large values of time even if a layer of coating is present on the hot wire. The significance of this result is that the thermal conductivity of an electrically conductive fluid can be measured with a coated hot wire using the same conversion relation as for a bare wire.