This is a fairly easy calculation if you know the temperature of both the stream and the add-water, know the stream flow rate, and assume complete mixing. (also assume no ice) Others can correct me if I'm wrong, but I believe it reduces to a weighted average based on volumetric flow rate:
(Combined T) = [(Stream Q)*(Stream T) + (Add Q)*(Add T)] / [(Stream Q)+(Add Q)]
..then solve for (Add Q)
I don't see why that wouldn't work. As others mentioned, best to ask the folks who do thermo for a living.
If you can't assume complete mixing, it gets horribly complicated. There are a number of other factors I'm neglecting which can also make this horribly complicated, such as sunlight warming, or pesky old hydrology.
I'm not an enviro guy, so I'm not sure what passes for acceptable practice in the field of effluent discharge. I'm just answering from a pure fluid mechs standpoint.
Hydrology, Drainage Analysis, Flood Studies, and Complex Stormwater Litigation for Atlanta and the South East -