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    $\begingroup$ Man, have you ever heard of a water-cooled radiator, or a geothermal plant? Essentially you describe a problem as not being able to radiate heat into the sludge with resultant overheat. Wrong, say 80286 PC did not require external cooling at all, and here in 2022 we have immersion-cooled devices with radiators elsewhere - these could be developed to transfer heat to sludge even if it's solid. $\endgroup$
    – Vesper
    Commented Nov 24, 2022 at 13:14
  • $\begingroup$ Faraday caged computers solve this pretty neatly. $\endgroup$
    – Daniel B
    Commented Nov 24, 2022 at 13:43
  • $\begingroup$ @Vesper Ah you're right. There is no reason to pump the sludge itself around as coolant. Just pump water through sealed tubes from the processor into the sludge and back. $\endgroup$
    – Daron
    Commented Nov 24, 2022 at 15:08
  • $\begingroup$ @DanielB Hmm. . . Will Faraday protect you against every form of radiation that could possibly harm you? What about neutron showers? $\endgroup$
    – Daron
    Commented Nov 24, 2022 at 15:08
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    $\begingroup$ @Daron great, so build something underground and cover the roof with a few meters of it. $\endgroup$
    – Daniel B
    Commented Nov 25, 2022 at 16:43