Limitations of temperature in a large body of water

In a river, water flows so how does it resist freezing? Or does it freeze at the same rate just that at the point where the cooling agent is at, the water keeps getting replaced. So the average kinetic energy of all the water molecules drop so as a whole the temperature drops?

But a river is huge so if I place a thermometer in one area and then in another, there's a good possibility that the 2 readings are different. So I'm quite confused about how temperature works. Temperature is the average kinetic energy of all the molecules but what are the limits to this?

Thanks for the help :smile: