So I went down, filled a sippy cup with milk, added a bit of vanilla at museinred's suggestion and brought it up to a slightly warm temperature. And I gave it to Katie and she went to bed.
Not too much later, she walked into our room and informed us that the sippy cup was too hot and too cold.
Uh huh. So she drank pretty much no milk last night, but she did go to bed. The sippy cup went in the fridge for later.
And not having consumed twenty to forty ounces of liquid immediately before bedtime, it was a pretty dry night. :)