AMD seems to design their components to get all the way up to 95 and sit there. It happened in the stock cooler for the 3600, and it happens on my 5700xt, even though I went for one of the nicer cards. It's still below the safe junction temperature, and it won't fry, and it can even run just fine like that for several hours.

The downside is that there is evidence that such high temperatures increase electron migration (or something similar) in the chips themselves, leading to not infinite lifetimes. I want this computer to last 10 years, so I bought an aftermarket CPU cooler for $30 to keep temps closer to 50 degrees

Not generally in the short term, but over the longer term increased heat is going to make it more likely that the chip fails prematurely.

Of course, if you do something like not attaching the heatsink at all, it's plausible that heat could spike fast enough to cook the chip before throttling or overtemp protection can kick in/shut the system off.