How does the rate of temperature change depend on the temperature difference between the two beakers?

By water evaporation from the leaves is created a negative pressure at the top of the tree that promotes the ascension  of the water through channels that are called xylem. there are also two molecule forces that are involved: the intra-water molecules cohesion (water molecules stick to each other) and the adhesion when the water molecules stick to the channels they are running in. this is what enables water to go from the roots to the top of a tall tree.