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I suppose the temperature would increase very briefly depending on how violently the ice was added. Carefully and slowly adding ice to water in order to minimize the water's displacement would, by definition, add kinetic energy to the localized water, but probably not enough to heat the water up. That kinetic energy would go towards breaking more bonds from the ice. However if you propelled the ice really fast into the water, one can only assume that the instantaneous increase of kinetic energy gained by the water would be greater than the kinetic energy being used to melt the ice, therefore (briefly) increasing the temperature.

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Q: Why does the temperature of water increase briefly when ice is added?
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