text: depends on room temperature, and on other factors, but...\n\nmost of the time boiling to room temperature will go very quickly compared to frozen to room temperature. Let's assume that you are talking about water, or things containing a lot of water like soup.\n\nPart of the reason boiling cools faster is that boiling things are releasing their hottest bits (molecules) up into the air above the container. When the hottest water leaves the container, what's left is actually colder. This is why water splashed on your skin very quickly feels cold even if it was warm at first. Evaporation is carrying away the heat.\n\nThen, the other main reason has to do with the nature of ice. Ice is a crystal, and it takes energy (heat) to break the bits of the crystal apart and turn them into water. So, ice will soak up a lot of heat in order to just melt, without the temperature even changing. After enough heat has been soaked up to break down the crystal, then the water remaining will begin to to start warming up to room temperaure, but without the benefit of the boiling/evaporation effect discussed above.