How do you expect the water level to change when the apparatus is placed in warm water? In cool water?

I am assuming that the apparatus you're referring to would be a container wherein there is water placed inside. To answer your question, I expect the water level to rise when it's placed in warm water and I expect it to fall when placed in cool water. This is because the water molecules get excited when placed in water molecule, thus, moving with more kinetic energy. The opposite goes with cool water.