Sure, but in this case, I would have expected "protecting itself" to mean "shutting down." Can a server CPU—or any x86 cpu, for that matter—actually downclock itself enough to run without any sort of cooler?
486s were sometimes passively cooled. A room full of hardware replaced by a very early virtualization setup lines up reasonably well.
I did one of these in the early naughts. Something like half a rack of old pentium 2-3 era boxes running non-prod — back office, network share storage, dev, staging — to a single beefy server running some flavor of vmware. We had all the older gen hardware for isolation and convenience, not because we needed the compute so I specced a “big” box that could hold a lot of storage (for the time) and performance was a non-issue. I think I also saved a lot on Microsoft licensing which made budget for the hardware.
In the early 2000s we had a mail server running on an old recycled Cyrix 5x86. When we had to move offices someone knocked down the wall next to the server but as it turned out the Ethernet cable was stapled to the wall and the machine went flying. Whatever, pack it up and move to the new office, plug it back in and it works fine.
About a year later we were rearranging some stuff and someone powered it off and picked it up to move it… and heard a rattle inside. Pop the cover off and the CPU cooler is sitting in the bottom of the case and the CPU is just sitting there naked. Had absolutely no problem running without the fan at all. We clipped it back on anyway just to be safe :)
There are a few videos on YouTube showing CPUs running without a heatsink. I haven't watched them to see how long they can run for, or if any BIOS changes were needed (I noticed the first mentions a lower voltage needs to be set to boot into Windows), but it seems possible at least.
There are also comments that claim to have done this (the oldest I saw was a Q8200, and someone said a 3000G could be run indefinitely without a heatsink).
I was playing Cities: Skylines on my old desktop PC a couple of years ago and the frame rate was really low. Windows was running sluggishly but mostly fine. I downloaded CpuZ to figure out what was going on with Skylines, and noticed that the core frequency was way lower than it should have been. I poked around in software for a while but couldn't figure out what was going on ... until I opened my case and realised that my CPU heatsink was dangling off the CPU, the top mounting pins having come loose.
So, yep, CPUs - at least 2014-vintage Intel Core i5s - can run surprisingly well without cooling!
I've heart that Intel CPUs can (often?) function (sloooowly?) without a cooler, while AMD CPUs will burn up. Perhaps the latter's temperature sensors aren't necessarily close to the major sources of heat, so the chip burns up before it notices that it's burning up. (And a cooler spreads the heat out so that the temp sensors see the real temperature.)
