in nature, would never experience consistent temperatures (well most anyway). there seems good evedence, on here anyway, that it not only does not do any harm to use cold water, it may well be enjoyable to the fish(if not actually being beneficial.
In nature, any change of temperature would be gradual. i.e. night time drop, heavy rains flowing down river etc etc.
Although not absolutely accurate, i did a test. Measured out 1 gallon of water, got it to 28.1 degrees, drew off 33%, added the equivalent water back in straight from the tap. Within a few seconds (digital thermometer) i saw a 6 degree drop to 22.1.
I then repeated this with a 40% change and witnessed a drop of 8.6 degrees.
I can tell you my bettas would not be happy
I would also say that these temps are a result of the water mixing, and that any fish directly in the influx of new water may be subjected to temps a lot lower. My tap water is approx 11 degrees c, so theoretically there could be anything upto a 17 degree shock for my fish.
Also, I dont actually see any evidence to suggest it may be beneficial to the fish. Maybe thats just what people want to believe to justify the action?