Why does the temperature of a substance not change while it is melting, even though heat is being supplied?

While a solid is melting at its melting point, the heat supplied:

Calculate the heat needed to melt 100 g of ice at 0 °C into water at 0 °C. Take the specific latent heat of fusion of ice as 336 J g⁻¹.

Why is water used as a coolant in car radiators and in industrial cooling?

Why is a burn caused by steam at 100 °C more severe than one caused by water at 100 °C?

Calculate the heat needed to raise the temperature of 200 g of water from 20 °C to 100 °C. Take the specific heat capacity of water as 4200 J kg⁻¹ K⁻¹.

Calculate the heat energy needed to raise the temperature of 200 g of water from 25 °C to 75 °C. (Specific heat capacity of water = 4.2 J g⁻¹ °C⁻¹)