* Their temperatures become equal. There is no longer a temperature difference driving the heat flow.
* The net heat transfer is zero. While there might still be some microscopic heat exchange, the overall amount of heat moving from one body to the other is balanced.
Think of it like this:
Imagine two cups of water, one hot and one cold. When you put them in contact, heat flows from the hot water to the cold water. As the hot water loses heat, it cools down, and the cold water gains heat and warms up. This process continues until both cups of water reach the same temperature. At this point, there's no more "driving force" for heat transfer, and the flow stops.
Important Note: While the net heat transfer stops, the molecules in both bodies still vibrate and possess internal energy. They are simply vibrating at the same average rate, resulting in the same temperature.
