Check that she's got a nice empty crop in the morning, so before she's had a chance to eat or drink - get out there and make sure she emptied overnight.
If she's empty in the morning, the water coming back up could very well just be the chicken trying to cool herself with lots of water. Chickens can only cool themselves by drinking water, panting, and holding their wings away from their bodies.
Because this year in Oregon has been so terrible with heat wave after heat wave, I gave up and put an air conditioner unit in my coop with furnace air-filters over the air-intake areas. The furnace filters have to be changed daily so the coop dirt doesn't kill the A/C, but the pay off is the 100+ chickens sleeping comfortably tonight and every night since I got it- which means I get to sleep!
I've done all the watermelon and cool water possible, deep shade galore - but when the temperatures don't cool off overnight- it's still nearly 80 degrees at midnight here - they just don't get a break and they're doing everything they can - including overdrinking- to stay cool. Obviously in hotter parts of the country people select more heat-tolerant birds. I never thought I'd see heat wave after heat wave up here like this - and I have the birds I have, selected for cool rainy weather ... not ongoing heat.
I used to look for the worst-off birds, usually my bigger, heavier feathered ladies, my older girls - and they'd get a 'motel' for the night in the basement in a crate so they could recover. And that was an OK solution when it was just a couple days over the course of the summer- and when the flock was smaller. So if you're able to give the ones who have the hardest time staying cool a break overnight inside in a cool spot, I recommend taking that step for them.