It depends. A 20 foot stream that's 10 feet deep and moving is a very difficult thing to heat up. Assuming the stream's water speed is roughly 7 ft/s (5 mph), that's over 1400 cubic feet of water moving through the stream every second, or almost 10,500 gallons. To raise the temperature of the stream by 5 degrees F takes 437,500 BTU's, or 128 kW's of power.
This is a lot of power, but not that much. It's equivalent to about 171 horsepower.
To continue, we now need the electrical resistance of the water. But here there's a problem. In a standard circuit, all components are of a small size with clear-cut boundaries. A resistor, for example, has clearly defined boundaries that make it relatively easy to calculate the resistance. A moving body of water, on the other hand, has no clear-cut boundaries except at where you place your electrodes. Basically, the current can run not only straight through the volume of water we just talked about to get to the electrode on the other side, but also up and then back down the stream, or down and then back up the stream.
The net result is that the resistance of the water is very low. Even our volume of water by itself has a resistance of only 0.286 ohms or so (using a resistivity of 1 ohm per meter as a compromise between the 0.2 of salt water and the 2-200 of drinking water). 128 kW's across this resistance equates to roughly 191 volts and 669 amps.
Note that all of the above calculations are very rough, use many simplifications, and were done by a guy whose a little rusty at solving these kinds of problems.