I took the heatsink all the way off and decided to put my knuckle on the die and boot up the machine. It took what felt like a millisecond for the die to feel 'nuclear' hot and the machine, thankfully, auto-switched off.
You're lucky you didn't get a severe burn on your hand or kill the CPU --- early AMD CPUs, notably from the late 90s / early 2000s, were infamous for catastrophically overheating without a heatsink. There's a video from Tom's Hardware showing that, after which AMD started adding more thermal protection.
(There are various assertions floating around that that video was fake, but given that no one seems to have made a "myth-busting" video in the 20+ years since it was released, despite the clear incentives for YouTubers to do so, and instead others have shown how hot those CPUs can get, I suspect it's real. Now that those CPUs and other hardware from that era are actually somewhat collectible, the likelihood of someone trying to repeat that video is even lower.)
I did think I had killed the CPU at the time, but being an impoverished student at the time I had no choice but to see if it was OK - and thankfully it was.
The heat was quick and intense enough that I took my finger off very quickly - it may have actually overheated and shut down faster than I took my finger (knuckle of my pinky) off, which might have saved me from a more lasting burn.
You're lucky you didn't get a severe burn on your hand or kill the CPU --- early AMD CPUs, notably from the late 90s / early 2000s, were infamous for catastrophically overheating without a heatsink. There's a video from Tom's Hardware showing that, after which AMD started adding more thermal protection.
(There are various assertions floating around that that video was fake, but given that no one seems to have made a "myth-busting" video in the 20+ years since it was released, despite the clear incentives for YouTubers to do so, and instead others have shown how hot those CPUs can get, I suspect it's real. Now that those CPUs and other hardware from that era are actually somewhat collectible, the likelihood of someone trying to repeat that video is even lower.)