>The resulting water is colder than the ice it came from and the water conducts heat better than ice, so the water warms up quickly until it gets warmer.

Thanks for this sentence. I couldn't get my head around how if something was colder it could still reach room temperature fasters than something warmer since the colder thing has to pass the warmer thing's temperature to get there. In my head it was the equivalent of "you can accelerate faster if you start rolling backwards".