Yes, I know. My hose is well water, not all that cold, so not an issue. It actually feels warm in the winter. And my sink water was cool, not cold. My buckets outside are also not all that cold, just cooler than the heat stroking chicken, and cooler than the ambient air.Just be very careful not to cool them down in cold water too fast and drop their temp too fast. This can cause them brain damage in a heartbeat. If you dunk them completely and drop their temp in say sixty seconds time over ten degrees this will do it.
I lost one last year and her core temp was about 118 degrees when I found her dead, she was almost too hot to touch.
Also, fat birds will have a lot more trouble with the heat, as well as any that have any underlying health issues.