Molten salt FLiNaK, that is a mixed fluoride salt of LiF, NaF, and KF, is considered to be a candidate of a coolant of nuclear fusion reactors. Until now, thermal conductivity of FLiNaK had been evaluated experimentally by means of several methods, and also numerically. However, their literature data differ in a wide range. Even some of the literature data are contradictory. Yet there has been no reliable database of FLiNaK thermal conductivity due to its high melting temperature, and chemical reactivity. In the present study, a new apparatus was fabricated to experimentally evaluate the thermal conductivity of FLiNaK at approximately 773 K by means of a transient hot-wire method. An advantage of the transient hotwire method is that it is able to detect if natural convection occurs, and avoid overestimation by the natural convection. Yet the transient hot-wire method has not been employed for FLiNaK. Its initial experimental result is given in the present paper.