You could try drinking a little more before bed to see if it reduces your thirst the next day. Sure, this’ll probably lower your temperature a bit that night, but it may help to keep it higher the following morning. Keeping it more even like this is ideal.
Additionally, you could try having some fairly salty water/juice in the morning. I find it helps me if I’m thirsty and need to drink but know it’s going to cool me off too much.