My water is aged in buckets before going in the tank, so it's room temperature. The tank is usually only 8 deg. F. warmer than the room, and at a 25% WC, the delta should only be around 2F. When I check my thermometer after a WC, it's usually 1-2F colder. I figure in nature, a rain storm might do something similar. That said, some fish are probably more delicate than others.

Any time I've used un-aged water, I tune the faucet a bit and hand-test the tap water before it hits the tank to make sure it's similar.

In homes with water softeners, the cold and warm taps might give you different water (one softened, one unsoftened) depending on the plumbing - so be aware of this where applicable.