I've not personally encountered circulators that run on 12V dc, but its plausible that they exist. I would personally seek a standard pump and convert the 12v dc to 120 ac as you will likely need to source replacement pumps in the future, and it would be sensible to keep the cost down.
So far as the 'heat rises' rationale goes, heat spreads through conduction, convection or radiation, you've just planned on convection. Thinking of the earth below as a heat sink is correct, but that can work to your detriment so far as energy consumption is concerned as it will keep on absorbing heat.
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"The trouble with people idiot-proofing things, is the resulting evolution of the idiot." Me
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