Every situation is different, if I was in the heat I would be drinking as much water as I felt I needed (a lot), and would not let myself get dehydrated.
However, most of my my solo shows were at an indoor mall show, climate controlled, I did them for 10 years, after 8 years of practice working in a small store where I would have to work 5 hour shifts by myself without breaks, I know my own body and my bladder.
Tana, you wrote that you were out of bottled water at home. Is your tap water not clean? We use our Brita water pitcher, half fill our thick plastic water bottles, put them in the freezer, then top them off with water, stick them in the cooler with some ice packs. I don't buy bottled water unless I am desperate, and will refill from the tap, or water fountain during the show if it's necessary.