Thermal equilibrium between two objects exists when their temperatures are equal. This means that the rate of transfer of thermal energy (heat) between the two objects is equal in both directions and there is no net transfer of heat from one object to the other.
When two objects are in thermal contact, heat energy will always flow from the object with higher temperature to the object with lower temperature. This will continue until the temperatures of both objects become equal. At this point, thermal equilibrium is established, and there is no net flow of heat energy between the objects.
Therefore, the correct option is "the temperature of both objects are equal".