Study the temperature changes when water changes phases. it can go well below freezing before it actually starts freezing, then warms as it goes solid.
Same when it melts. It has to absorb a great deal of energy and go over 32 degrees to actually melt.
I worked on a project back in the 80's to STORE that phase change energy at night and use it to cool during The day.
They used a spacial salt water that exaggerated the delta T for the phase changes. Neat stuff.
Zero Energy Offices, phase change materials for hvac applications
EDIT: the temperature does not change during phase change, but the amount of energy absorbed or given up swings during phase change. Ice absorbs a great deal of energy while it melts, and water gives off a great deal of energy as it freezes.
that's what i meant but did not remember all the details.