I had the same inclination back in the 90s when I upgraded my Cyrix 486 SLC2 50MHz without a heat sink (which seems like a no-no in retrospect) to Cyrix MediaGX 133MHz. The stocker fan was immediately noticeable. I thought I had done something wrong.
Upgrading and Repairing PCs 4th edition even says directly, that some shady resellers will put a heatsink on a chip that they're running beyond spec, but that Intel designs all their processors to run at rated speed without one.
The cpu and heatsink was fully integrated into what looked like a NES cart, with an integrated fan and everything. It was not really possible to separate the cpu and the heatsink as the locking mechanism to keep the cart in place on the motherboard interfaced with the heatsink assembly.
So I'm a little dubious of that no-heatsink claim.