text: One statement of the so-called zeroth law of thermodynamics is directly focused on the idea of conduction of heat. Bailyn (1994) writes that "the zeroth law may be stated: All diathermal walls are equivalent".
  A diathermal wall is a physical connection between two bodies that allows the passage of heat between them. Bailyn is referring to diathermal walls that exclusively connect two bodies, especially conductive walls.
  This statement of the "zeroth law" belongs to an idealized theoretical discourse, and actual physical walls may have peculiarities that do not conform to its generality.
  For example, the material of the wall must not undergo a phase transition, such as evaporation or fusion, at the temperature at which it must conduct heat. But when only thermal equilibrium is considered and time is not urgent, so that the conductivity of the material does not matter too much, one suitable heat conductor is as good as another. Conversely, another aspect of the zeroth law is that, subject again to suitable restrictions, a given diathermal wall is indifferent to the nature of the heat bath to which it is connected. For example, the glass bulb of a thermometer acts as a diathermal wall whether exposed to a gas or a liquid, provided that they do not corrode or melt it.
  These differences are among the defining characteristics of heat transfer. In a sense, they are symmetries of heat transfer.