At such large die scales and high temperatures heat engines become practical as a means of both cooling and also extracting work. I wonder if there is serious research in this area?
IIRC they become less efficient at higher temperatures, as the thermal-induced noise increases (might be as part of sub-threshold leakage; I don't remember the details).
There are considerable efficiency gains from running silicon CMOS at LN2 temperatures instead of room temperature, but the benefits fall apart once you realize you'll have to heat-pump the electrical consumption from 77K to room temperature. Main benefits would be being able to run them faster, and a good part of the optimization would need lower dopant concentrations in the transistor channels to properly take advantage of the low temperature, which unfortunately rules out common shared-wafer prototyping runs (so testing this IRL isn't really accessible).
