If you're waking up every night between 2:00 and 3:00 AM with a dry mouth and it's not related to the air-conditioning, it would be worth going to see a doctor and getting checked out for the following:
- Diabetes insipidus (which is not the "regular" diabetes melitus)
- Cortisol levels. If they spike during the night due to blood sugar or other issues, you can wake with a jolt, and it can be very hard to get back to sleep.
- Adrenal fatigue (can cause you to wake around that time and again, really struggle to get back to sleep)
- Liver function issues (your liver works hard when you're asleep and any problems can cause you to wake between 1:00 and 3:00 AM)
I had exactly the problem you describe of waking up at that hour and it took a year to get to the bottom of it. It was a combination of adrenal fatigue and gut issues.
Of course, it might just be an issue with the air-conditioning and the humidity in the room. I hope that's what it is as that is an easy fix.