TCB,
I can say that in a river due to the moving water there will not be a thermocline. Even on the St. Johns which has fairly slow water. It is enough to mix up the water sufficiently to keep thermoclines from forming.
Here is a definition courtesy of Wikepedia:
The thermocline (sometimes metalimnion) is a layer within a body of water or air where the temperature changes rapidly with depth.
Because water is not perfectly transparent, almost all sunlight is absorbed in the surface layer, which heats up. Wind and waves circulate the water in the surface layer, distributing heat within it somewhat, and the temperature may be quite uniform for the first few hundred feet. Below this mixed layer, however, the temperature drops very rapidly—perhaps as much as 20 degrees Celsius with an additional 150 m (500 ft) of depth. This area of rapid transition is the thermocline.
Thermoclines can also be observed in relatively shallow lakes. In colder climates, this leads to a phenomenon called turnover. During the summer, warm water, which is less dense, will sit on top of colder, denser water that sinks to the bottom, with a thermocline separating them. Because the warm water is also exposed to the sun during the day, a stable system exists and very little mixing of warm water and cold water occurs. One result of this stability is that as the summer wears on, there is less and less oxygen below the thermocline, as the water below the thermocline never circulates to the surface. As winter approaches, the temperature of the surface water will also drop until it approaches 4 °C (39 °F), which is the temperature at which water is densest. 4 °C is, generally speaking, the temperature of the water below a thermocline. When the entire body of water is at or close to 4 °C, 'fall turnover' begins - the thermocline disappears, (or, to say a different way, it reaches the surface) and the water from the bottom of the lake can mix freely with the water from the top. This process is aided by wind or any other process that agitates the water.
As the temperature continues to drop, in those locations where it does, the water on the surface begins to get cold enough to freeze and the lake begins to ice over. A new thermocline develops where the densest water (4 °C) sinks to the bottom, and the less dense water (water that is approaching the freezing point) rises to the top. Once this new stratification establishes itself, it lasts until the water warms enough for the 'spring turnover,' which occurs after the ice melts and the surface water temperature rises to 4 °C.