It hadn't occurred to me that while there would be no actual ice cubes, the water would still be ice cold.
So when the waitress came back around, I said, "I don't mean to be difficult, but is there any way I could get water that's closer to room temperature? I had dental surgery on Monday and am really sensitive to cold."
"Oh, I'm so sorry!" the waitress said (and it was clear that this was sympathy, not apology). "That's all I have out here, but let me see if I can figure out something in the back."
A few minutes later she returned with a new glass of water from the kitchen. It was actually a bit warmer than room temperature, which was absolutely fine with me.
Granted, it seems like a very small thing, but our group arrived just as a huge rush started, so I was very grateful that she was willing to make an extra trip back to the kitchen to find warmer water for me. And, yes, I did thank her both verbally and with the amount of the tip.