"Most liquids have a quite simple behavior when they are cooled (at a fixed pressure): they shrink. The liquid contracts as it is cooled; because the molecules are moving slower they are less able to overcome the attractive intermolecular forces drawing them closer to each other. Then the freezing temperature is reached, and the substance solidifies, which causes it to contract some more because crystalline solids are usually tightly packed.
Water is one of the few exceptions to this behavior. When liquid water is cooled, it contracts like one would expect until a temperature of approximately 4 degrees Celsius is reached. After that, it expands slightly until it reaches the freezing point, and then when it freezes it expands by approximately 9%."
Looks like the water/coolant level should go down as it cools unless it is near freezing outside but then antifreeze probably affects this behavior.
I was curious when you asked if water expands as it cools so I did a little research
. I knew that it contracted when it cooled and expanded when freezing because of the crystalline structure of the molecules but didn't know what at what point the cooling water started to expand.