I question whether with water would actually get any flow through the system in a loop, especially against gravity. Seems like you might have cool water moving from the cooling tank back to the warming tank at the same time warm water is moving up...IF the temperature differential is great enought to generate such convection currents.
Otherwise the heat transfer would be mostly radiation and conduction...
Heat Transfer
Also, if the system is a closed loop full of water, heating up one side of it would just cause an increase in pressure throughout the system. If you heat it up enough, it would explode.
