This wouldn't make the room any cooler, though, as the total energy used by the computers is the same. It would just dissipate the heat in the air, rather than keep it on the chips.
I feel like that might be embedding some questionable assumptions, such as:
1. That CPU computing work completed is directly proportional to joules of heat emitted.
2. That stymied active cooling measures don't themselves generate heat, such as all the fan motors spinning at 100% and the AC/DC conversion to power them.
3. That even if performance was improved by removing thermal-throttling, demand would still push everything to run at full-tilt rather than allowing some machines to idle.
Unless the work to be done is unlimited, all else being equal, hopefully a well functioning system puts out less heat to do X amount of work than a poorly running system.