A diathermal wall permits heat transfer. For a clean zeroth law of thermodynamics comparison, idealize it as rigid and impermeable, excluding boundary work and matter transfer. A thin metal partition approximates this arrangement.[ref]
4 Classical Thermodynamics. §4.1, printed p. 109: rigid, particle-impermeable diathermal walls and the thin-metal example
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A diathermal wall is a type of barrier that allows heat to flow freely across it. In thermodynamics, it is used to describe a wall or boundary between two systems (or a system and its surroundings) that does not impede the transfer of thermal energy. In contrast to adiabatic walls, which prevent any heat transfer, diathermal walls enable energy exchange in the form of heat.