Compare the temperature of water as ice begins to form with the temperature of ice as it begins to melt

They are the same temperature.

If you have 1 gram of ice  at zero degrees C, you have to pump 334 joules
of heat energy into it in order to just change it from solid to liquid at the same temperature.

This is one of the highest figures known for any substance, and that's why
a piece of ice does such a good job cooling your drink.

The geological theory that states that pieces of earth's lithosphere are in constant slow motion is the theory of plate tectonics.