An empty frige uses the least energy only because there is no need to plug it in. An almost full fridge is the most efficient state. The mass of cold solids and liquids hold heat better than air alone.
If you go with the water jug idea, fill the jugs with the water from the shower the next time you are waiting for the water to warm up. In summer, when jugs are unused, keep them in the basement or other cool place. In the winter perhaps an enclosed porch.
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