Natural bodies of water that support fish life rarely change more than half a degree a day in temperature
With a lake sized body of water thats true, but for a small river the temp can swing a lot on a daily basis.
This page is flow and temp readings of the Patea river that flows through my home town.
http://www.trc.govt.nz/environment+online/river/patea+skinner/patea+skinner.htm
Todays graph (near the bottom of the page) with the last 7 days data shows temp variations of 10deg C over the week and up to 5 deg C on a daily cycle.
Now it's true that you dont want the temp swings to be too extreme or go outside what the fish can handle, but obviously the local fish can handle 5C change per day and probably 20C change over the seasons.
Cheers
Ian