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I see no obvious way. Perhaps putting the thermo-regulators into a steam room. They seem to just dump their heat wherever. If some of their heat is required, then it shall be transferred in a controlled manner from the steam room. I'm not sure about how some details of those design work but, in the second one, they seem to work against the counter-flow heat exchanger by dumping heat into incoming material.

The design is upside down. In ONI that are certain "heat rises" mechanics which means that "cold on bottom, hot on top" setups maintain stronger temperature gradients which improves the efficiency of counter-current heat exchangers, in particular with gases, the rule is that for two gas tiles of the same type, they are allowed to swap places vertically only if the colder one is on top (if the gas tiles are of different types then "density" based swapping rules take precedent). So hot gas tiles will swap their way up a colder column.

This becomes especially important as gas pressures increase, the basic reason for this is that conduction based heat transfer between gas tiles is basically independent of mass (unless we're talking really low mass tiles), but "swapping based heat transfer" is directly proportional to mass, this means if your counter-current heat exchanger is "cold bottom, hot top" you can pretty much run it at any pressure you like without substantially degrading performance and also the heat exchanger can be shorter.

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