We demonstrate a liquid-state thermal diode in which the thermal conduction changes through thermal expansion of metallic liquid to displace air. The forward (high conduction) mode occurs when the liquid spans the diode to produce a highly conducting path. The reverse mode occurs when the hot side is adjacent to air in the diode. The air provides a large thermal resistance so that the liquid metal in the reverse mode is at a lower average temperature than in the forward mode, and thus the liquid does not span the diode. With a prototype device using mercury and air in a glass tube, we demonstrate that the thermal resistance between the forward and reverse modes can differ by a factor of two, giving a rectification coefficient of about one. The rectification occurs at a variety of temperatures, and increases with the temperature difference across the diode. A figure of merit for selection of the liquid is the product of the liquid's thermal expansion coefficient and thermal conductivity. Mercury was chosen because of large values of both of these properties, and the ability to wet and dewet a surface. (C) 2016 Elsevier Ltd. All rights reserved.