It doesn't get you anything, there is never any reason to pump something below ambient in heating.
Oh dear, i hope you don't need to use physics for your day job...

The beauty of storing heat energy at a constant temperature is that you can manage the losses, because those loses are driven by the thermal graident to the ambient environment.
For example, i have two cups of water on my desk, in a room at 25 degC. The water in one cup is at 50 degC, the other is at 25 degC.. Which cup looses more energy to it's environment ?
Solar hot water heating panels normally have to tread a fine line, they have to allow as much solar radiation into the coolant medium, but let as little heat energy escape. Up on your roof it's probably cold, and windy, if the solar radiation heats the water in the panel to say 50degC, then that's significantly higher than the environment, so no matter how good the insulation is, some of the heat energy gathered from the radiation is lost.
Now consider a panel where the water temperature in the panel is not allowed to get above ambient. What are the loses now? Can you see the advantage?
Of course, the trade off becomes a balance of the CoP of your thermal converter (heat pump) vs the delta T of the system. The higher the deltaT, the lower the CoP (RE: carnot cycle efficiency).
This is what i shall run some simulation to characterise, as there is plenty of data on practicalable heat pump CoP vs deltaT with different refrigerants.
The single benefit of a water storage system is however cost, or lack of it. Using a thermal temperature converter allows you to utilise low level heat, and that means cheap storage. My 1000 litre ICB, with a working temperature range of +- 25degC from ambient contains the same amount of energy as a big Tesla Battery (~100kWh) and yet the plastic tank costs around $100 and the water in it is effectively free! It also can be charged and discharged an infinite amount of times, and the charging rate, thanks to the higher specific heat capacity of water is actually pretty good too