Who says memory has to be made of transistors? In the past, memory has been made of ripples on mercury, ferrous donuts, rotating drums, holes in paper, glow in phosphors bombarded by electron beams... storage need not run hot. In particular, bits not changing state need not consume any power. Changing state may take arbitrarily little power; the faster they must change, the more power it usually takes, but write speed is less critical than read time. Interacting with it is always going to take power and produce heat, but that may be much, much less than with masses of transistors.
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