http://www.intel.com/content/www/us/en/support/processors/000006710.html
"Allowing processors to operate at temperatures beyond their maximum specified operating temperature may shorten the life of the processor and can cause unreliable operation."
"Proper "thermal management" depends on two major elements: a heatsink properly mounted to the processor, and effective airflow through the system chassis. The ultimate goal of thermal management is to keep the processor at or below its maximum operating temperature."
"The heatsink included with the boxed Intel Xeon processor must be securely attached to the processor. Thermal interface material (applied during system integration) provides effective heat transfer from the processor to the fan heatsink.
Critical: Using the boxed processor without properly applying the included thermal interface material will void the boxed processor warranty and may cause damage to the processor."
These are all Xeon docs, but I doubt if the consumer CPU documentation is substantially different.
Edit: I have in front of me, the little pamphlet manual that comes with a Skylake Pentium G4400 CPU, labeled "Intel Pentium Processor". It lists "Installation instructions". Unfortunately, it's all in pictures. I could have sworn I remember past little manuals stating that their processors "were not to be operated without heatsink and fan attached".
But I searched this manual, and I couldn't find that wording.
I just remember (all too well), that TH video, with the P4 and Athlon XP, with what happens when you remove the heatsink. P4 slowed way down and throttled, AXP basically blew up. Then again, some people said that video was intentionally faked. I don't know for sure.