I am not sure that it is quite that simple.
You do need water to aid in digestion, and digestion is what provides all the warmth in your body. However, I doubt that ordinary thirst would make much difference when you are lying down (exercising may be different). There's an awful lot of water in your body even when you are thirsty.
I suggest that a significant effect is that when you are thirsty you just can't relax as well. So you stay awake and squirm around and that makes you get cold.
But, this is just a thought, based on how people get cold when they are trying not to go to the loo at 2 am. There may well be physiological factors I don't know about.