Having thought it through a little more, I've realized that I was doing some muddy thinking. If all the molecules in some water are moving in the same direction, it won't affect the effective water temperature at all. To state the obvious, a glass of water in a jet plane doesn't boil a when the plane takes off, and yet the water molecules are all moving rather quickly! It's all to do with how fast they are moving relative to each other - their tendency to fly apart. This does not change for the water in the glass in the jet, and out won't change either for flowing water (apart from the valid comments made about the heating effect of the moving water coming into contact with eg the edges of whatever it it's in)