First, remember that heating and cooling are all about flow of heat energy. Heat always flows from hotter to colder objects, and importantly, it moves faster if the difference in temperature is larger (aka the temperature gradient.) Think of how cars roll slowly down a gentle slope, but quickly down a steep slope–the difference in elevation works the same way. Also, some materials conduct heat a lot faster than others, so heat flows in/out of them faster. Air isn’t that great compared to water, and metals are better than water.
So, think about a mug of hot water, maybe 150 F (60 C) sitting in a room-temperature room (71F or 22 C.) It will slowly lose heat to its surroundings, because the difference in temperature isn’t that big. It’s also losing heat to air, which is fairly slow, and doing it from a smallish surface area. By the way, we tend to use materials for mugs that are bad at conducting heat, because that keeps drinks hot longer and stops your fingers from getting burned, so the mug is making it cool slower.
Now, if you pour room-temperature water into a kettle that’s heated to 400 degrees, you’ve got a much bigger difference in temperature, and you’re using hot steel to rapidly dump lots of heat into water. The water heats quickly.
We can absolutely cool things down quickly. If you took a big frozen silver pan and poured the mug of water into it, it would cool in no time, because you’ve got a bigger temperature difference, better conduction, and more surface area.
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