Are there any perks in keeping a CPU at a low temperature; between 0 and 20 degrees Celsius in particular?
In particular, does it produce less errors in computation and therefore slightly improved performance or response time?
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If a CPU produces any errors at all in computations, we consider it "broken". If the CPUs temp specification gives it's normal operating temp range as 0 ~ 95 ˚C (for example) it will produce no errors over this entire range.
However, in general, semiconductor devices will draw less power at lower temperatures, so, ironically, if you spend some power to cool them, they will consume less power. This is usually not a very important attribute except to heat sink and power supply designers.
Digital logic propagation times usually decrease with decrease in temperature, i.e. the gates get "faster". Theoretically, you could increase the clock frequency of a CPU if you were to keep it cooler compared to when it was hot. This would of course make your computer faster. But you can't get fewer than 0 errors ;)
Very few designs of CPU are able to adjust their speed of operation based on continuous variations in the speed of the internal logic. Where this has been tried, its likely to be purely for research projects. Such a design might be termed asynchronous (even if it uses variants of classical sequential cells and a recognisable pipeline structure) due to the lack of a common distributed clock.
A cooler CPU will (all other things being equal) last longer in running hours. This is more significant at elevated temperatures, usually quite a small effect, and only likely to be noticeable at smaller geometries. Running at elevated voltages would have a much more significant impact on lifetime (but in a constrained temperature range, undervolting would be more feasible).