Whilst Demon's don't need blood or a beating heart to keep them alive, moving blood around their body helps keep all of them a consistent temperature, and either warm them up or cool them down by pulling blood away or towards the skin, like is done by us humans, which is useful when you're living in the extreme climates of Hell.
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Black butler Headcanons
FanfictionJust some book filled with whatever Black Butler based nonsense my brain decides to cough up.