When an ice molecule hits a water molecule, the water molecule adds kinetic energy to the ice molecule. Why do the water molecules lose kinetic energy? In other words, why does heat like to go where there is less heat? I know thermodynamics tells us energy can't be created or destroyed. It doesn't really make intuitive sense, though. In the macroscopic world, if a ball hits a moving object in a non-opposing direction to the direction of force initially applied, the object's velocity actually increases, while the ball suffers from Newton's equal-and-opposite-reaction rule.
Basically a "molecule" of water cannot heat up ice.
I think what you are trying to say is, how does heat transfer take place on a molecular level? If that's the case, then its something like this. In the interface between water and ice, water molecules are moving, while ice molecules are static. on contact, some molecules of ice acquire velocity (due to no binding forces in one direction, and cohesive forces towards liquid water molecules). as a result, surface molecules of ice start acquiring velocity, hence changes state from solid to liquid (simply, ice melts). and due to conservation of energy, an equivalent amount of kinetic energy (macroscopically, heat) is lost by water. hence water cools a bit.
Of course there may be better ways to explain this, but i tried my best. hope you understand :)