How does conduction transfer heat through a solid?

In physics, thermal conduction is the process by which heat is transferred through a solid via molecular or atomic agitation and direct contact between particles.1

It is important to clarify that heat transfer by conduction does not involve the physical movement of atoms or molecules through the material. Instead, heat energy moves along a temperature gradient—from an area of higher temperature and greater particle agitation to an area of lower temperature and less agitation. This transfer continues until the material reaches thermal equilibrium, where the temperature is uniform throughout.1

The rate at which this energy is transferred depends on the material's thermal characteristics, the magnitude of the temperature difference, and the distance the heat must travel. This phenomenon was famously analyzed by the French mathematician Joseph Fourier, whose work on the analytical theory of heat provided the mathematical foundation for understanding how heat moves through solid bodies.12