What method of heat transfer occurs when heat flows from molecule to molecule within a substance?

The method of heat transfer that occurs when heat flows from molecule to molecule within a substance is conduction. This process involves the direct contact of particles, where the kinetic energy of higher-energy molecules is transferred to neighboring, lower-energy molecules. As a result, heat moves through solids, such as metals, very efficiently due to close packing of molecules and the ability of their vibrations to pass energy along.

In contrast, convection involves the movement of heat through fluids (liquids and gases) caused by the movement of the fluid itself, while radiation refers to the transfer of heat energy in the form of electromagnetic waves, which can occur through a vacuum. Evaporation is a phase transition where molecules escape from the liquid phase to the gas phase, which is not directly related to the transfer of heat between molecules within a single substance. Thus, conduction is the appropriate term to describe the situation presented in the question.