Unfortunately, it is not that easy.
Without a pump, there is no way to move the hot water from the hot water line into the cold water line. Remember, they are both equally pressurized by the line pressure from the supply lines. Without differential pressure -- ie., more pressure on the hot water lines than on the cold water lines -- there is nothing to move the water from the hot water line to the cold water line.
This solenoid valve is the basis for a commercially available type of system from Grundfos (also sold under the Watts name), but these also have to have a pump to supply pressure.
The main problem with these systems that use the cold water line for the hot water return is you often get warm cold water not only from the backflush from the hot water line but also from leakage through the by-pass valve when temp of the water in the hot water line is not high enough to close the solenoid.
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Check ourhotwaterrecirculatingsection for more Q&A on this topic.