I had a similar experience like yours about 6 years ago but it was with two of our Athlon 64 X2 chips. I bought my first K8-based CPU back in September of 2007 (X2 4800+) and just less than a year thereafter, around April or May 2008, the CPU temps just started to skyrocket all of a sudden. IIRC these chips normally ran at around 40C to 50C but then my 4800+ started to reach up to around 90C and the system would just shut down. Checked the HSF, which was even hotter than usual, which means there's no problem with heat transfer, fan seemed to be spinning fast enough based on the air blown, no voltage changes and they were all running at stock, no overclock, no voltage tweaks whatsoever. I cleaned the HSF, tried another HSF, re-applied TIM, checked case fans, nothing worked. Now, I should mention that after buying my Athlon 64 X2 4800+ I gradually bought more K8-based, 65nm Athlon 64 X2 chips/systems (I think there was one 5000+, another two 4800+ chips, a 5200+, and a single-core Sempron... 6 K8/65nm chips in all). I then took one of the other 4800+ chips from another system and used that in mine, which worked just fine and which temps were normal. So, it was the CPU. A few months thereafter another machine, this time using the 5200+ (or was it the 5000+?) started exhibiting the exact same problem too. This machine had different surrounding components (different mobo, video card, everything was different). Swapping the chip out for another one fixed the problem as well. So, conclusion, there seems to have been overheating issues with my 4800+ and the other 5200+. Contacted AMD for an RMA and they immediately acknowledged the problem. Sent the bad chips and less than a week later I had two brand new 5200+ chips straight from AMD Singapore. Guess AMD was aware that somehow their 65nm chips had this sort of problem. Never had a problem with my 45nm Phemom II X3 after 3 years of use and my current 32nm FX-8350 is just fine after 16 months of ownership.
My point is, I have the feeling that for some reason the dies themselves were getting hotter. Perhaps their electrical conductivity degraded over time such that they became hotter? The HSFs were getting really hot themselves and swapping the chips out fixed the problems for good. I can't think of any other reason why the chip temps shot all the way up on two different machines. Come to think about it, I think a third machine also had this exact same problem but then it was already on its way out for an upgrade (I think it was one of the replacement chips from AMD) so I kinda just shrugged and shelved it.
AMD FX-8350 / Gigabyte 990FXA-UD3 (rev. 4) / 2 x G.Skill Ripjaws 4GB DDR3-1866 / AMD HD7770 1GB / TP-Link WN723N USB Wifi-N / Samsung 840 EVO 250GB / Hitachi 7K1000.C 1TB / LG ODD / Cooler Master GX650 / Aerocool VS3 / LG W2252TQ / Win7 64-bit