I am (slowly) learning thermodynamics. I find a lot of it puzzling and makes me formulate many conjetures; I hope any of you can help me with this one about heat exchange. Let's start with this system: There is a closed hose loop filled with water; its temperature gradient goes from cold to hot from one extreme to the other. The system is perfectly isolated from the surroundings, but the hose makes contact with itself creating a heat exchanger. Water runs in the hose without friction, let's assume there is no pump / no pumping losses. The length of the hose is large enough for complete heat exchange. Cold water reaches the hot end at the same hot temperature, and viceversa. Questions: Would this system remain at the same temperature at all its points indefinitely? Or do thermodynamics require this system to evolve to an average temperature some way?