Final answer:
The direction of the exchange of thermal energy between two objects is determined by the temperature difference, with energy flowing from the higher-temperature object to the lower-temperature object until thermal equilibrium is reached.
Step-by-step explanation:
The property that determines the direction of the exchange of thermal energy between two objects is temperature. Specifically, when two objects at different temperatures come into contact, heat spontaneously flows from the object with the higher temperature to the object with the lower temperature. This is because thermal energy seeks equilibrium, meaning it moves in a direction that will eventually result in both objects reaching the same temperature.
Once the objects are at the same temperature, there is no net heat transfer between them. This state is known as thermal equilibrium. Therefore, the correct answer to which property determines the direction of thermal energy exchange is the temperature difference between two objects.