I think it would have to depend on the velocity of the current, or lack thereof. In a lake with little or no current, there would definately be differences in temp with depth. I believe they are called thermoclines, similar to picnoclines (spelling?), which are differences in water density. In a swiftly moving river I doubt there would be any thermoclines at all. In a slow or moderately flowing river there could be minor thermoclines, but probably not too much of a difference in temps. It might also depend on the depth of the river/lake in relation to the current speed. I'm not sure how fast the Amazon moves, or if it varies throughout, so I can't really answer your question, but there's something to think about. I'm sure fish do swim thru these thermoclines, but I doubt they do it very often, like for fun. There must be specific reasons for these migration patterns/habits, like changing weather, changes in disolved oxygen, etc. They are not forced to do so. That is why I think it does matter if your heater goes on and off. I'm confident that your fish would prefer a stable temp.
