Diathermal wall

A diathermal wall is an idealized system boundary that allows heat transfer between a system and its surroundings . In other words, energy may cross the boundary as heat, described by the inexact differential of heat $\delta Q$.

Physical interpretation.
A diathermal wall models good thermal contact (e.g., a thin metal interface) so that, when two systems are separated only by such a wall and are otherwise constrained, heat can flow in response to a temperature difference.

Thermal equilibration.
If two subsystems can exchange heat through a diathermal wall and the composite is otherwise isolated from the external environment, they relax toward thermal equilibrium , characterized (in equilibrium thermodynamics) by equality of their temperatures:

This operational role is tightly connected to the zeroth law : diathermal contact is the mechanism by which “having the same temperature” becomes an experimentally meaningful notion.

Contact with a thermal reservoir.
When a system is placed in diathermal contact with a thermal reservoir , the reservoir idealization implies the system can exchange heat while the reservoir remains at fixed temperature, so the system can relax toward $T = T_R$ (subject to other constraints).

What a diathermal wall does not specify.
Diathermal refers only to heat permeability. The wall may still be mechanically rigid (preventing boundary work) or movable (allowing work transfer), and it may be impermeable or permeable to matter depending on whether the system is closed or open .

Contrast.
A perfectly insulating boundary is an adiabatic wall , across which heat transfer is excluded.