As soon as the partition is removed, the immediate first reaction is that the clear cold water all sinks to the bottom, and the warm green water all collects on top. So at the beginning, you get a green layer sitting on top of a clear layer, with a sharp, distinct line between them.
As time goes on, heat starts to move from the warm water to the cool water. It happens right at the place in the middle where they meet, so it doesn't go along very fast. Little by little, some heat conducts out of some warm green water and into some cool clear water.
After a long time, all the water in the tank becomes the same temperature. It's all light green, and the convection (flowing up and down) stops.
