When I was younger I was told by a teacher at school that the quickest way to cool down something hot (it was a baking tray just taken out the oven), was not to put it under the cold water tap, but the hot water tap. How can that be so? Or was she wrong?!
Common sense should dictate that the easiest way to cool something down is to use something cool.
Take a computer heat exchanger or a car radiator, you wouldn't boil a kettle and stick it in your radiator would you? I think you teacher may well have just been one of those wacky sorts who would wear turn-ups and socks with sandles.
Difficult one this. Teachers are a strange breed. Who else would want to become a teacher, when you could become a dustman? How would she cool it down if there was no hot water available? Like most poor Northern homes our hot water is strictly regulated by the amount of coal we put on the fire. And this is normally done in the evening when the old man brings back a bag of stolen coal from the Pit. I suspect you would have to hold the hot baking tray until the kettle boiled. Never mind the third degree burns, at least you saved the cake(or hot-pot). Hope this helps.
Maybe your teacher was referring to things in general taken from an oven, and just happened to be removing a baking tray at the time?
Certainly, any glass or ceramic item shouldn't be cooled straight away with cold water, since it could crack or shatter. With a baking tray, I wonder. Perhaps pouring cold water on it could permanently warp the tray. There might be less chance of this if hot water was used instead?
All the answers give excellent reason for using different cooling methods in order to preserve the shap and quality of an item. The same can be said for warming something up, i certainly would'nt pour a kettle on a frozen windscreen like my uncle did as it would obviously break the glass.
As for the method of cooling ice cream, it's new to me, but i think we can safely say that if your pretty solid and not very expensive crockery plate is a bit warm we'd all run it under the cold tap.
Weekends coming up anyway so if you get bored at least you'll have something to aleviate it! ;-)
Maybe of interest this - we use a mixing vessel at work in which we need to cool down - it takes longer for it to cool down using cold water ( 5-10 degrees ) than it does with warmer water ( 20 degrees).