When an ice cube floating on water in a container melts, it is said in some textbooks that the water level does not change. However, as pointed out by Lan in a recent work, when the buoyant force from a less dense fluid resting above the waterline is taken into account, one should expect a detectable "increase" in the volume of water. Here in this work, by noting that the melting process itself reduces the water temperature, which in turn "reduces" its volume, we show that the thermal contraction of water can override the volume increase predicted by Lan. (Contains 1 figure and 6 footnotes.)