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Yes ,the higher the temperature gradient between the hot water and room temperature, the faster it cools.

However, that does not mean that hot water will freeze faster than cold water (a common urban legend). If you have water at 50°C in a room at 20°C, it will cool from 50° to 40° faster than it will cool from 40° to 30°.

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Q: Does hot water get colder faster than cold water?
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