Final answer:
The adjacent material must supply heat flow at a specified temperature to allow for the transfer of thermal energy. Heat flows from the substance with a higher temperature to the one with a lower temperature until thermal equilibrium is reached.
Step-by-step explanation:
At a specified temperature, the adjacent material must supply heat flow. This is because heat transfer, or the transfer of thermal energy, occurs between two bodies at different temperatures. When substance at a high temperature, with high thermal energy (H), comes into contact with a substance at a low temperature and low thermal energy (L), the thermal energy flows spontaneously from H to L. The temperature of H decreases as does the average kinetic energy (KE) of its molecules, while the temperature of L increases along with its molecules' average KE. This process continues until thermal equilibrium is reached and both substances share the same temperature.
In the context of the question, the rate of conductive heat transfer is directly related to the temperature difference between two systems. With an increase in temperature, there often is an increase in heat flow into a system. When thermal energy is transferred to cause a phase change, the temperature of the system might slightly change or stay the same, depending on the nature of the phase change.