How does heat energy affect the movement of water molecules?

Water is affected by heat energy by either freezing or vaporizing, depending on the type of energy.
Technically, heat is what we call the flow of thermal, kinetic . This idea is similar to calling a change in distance movement. One cannot isolate or change, we can only observe it. That being said…
The effect of heat on water depends on whether the energy is moving into the water (endothermic) or moving out of the water (exothermic). When water molecules gain energy, the average speed of the molecules increases; this is measured as a temperature change if enough energy is gained. Conversely, when energy leaves water molecules, the average speed of the molecule decreases, and a temperature decrease may be observed.
If enough energy is absorbed, the molecules may have enough energy to overcome the forces that hold them to each other (called intermolecular or van der Waals forces) and change phases. The inverse would be true if energy was removed; the molecules would lose enough energy that the attractive forces would be strong enough to hold the molecules together.
In short, if energy goes into water, the molecules will move faster. If energy is removed, the molecules will slow down.