* Temperature is a measure of the average kinetic energy of the particles within an object.

* Heat transfer occurs when there is a difference in temperature. Heat always flows from a region of higher temperature to a region of lower temperature.

In the scenario you described:

* The objects have the same average kinetic energy.

* There is no temperature difference to drive heat flow.

* The objects will remain at the same temperature.

Think of it like this: Imagine two identical cups of coffee at the same temperature. If you pour one cup into the other, the temperature of the coffee won't change because both cups were already at the same temperature.

Important Note: While there's no heat transfer, there may still be other interactions at the molecular level. For example, molecules at the surface of the objects might exchange some energy through collisions, but this would be negligible and wouldn't result in a noticeable change in temperature.