The 2011 issue is probably bad GPU, which affected entire industry for a while (2011 ThinkPads with discrete GPU had similar issues). A possible fix is to disable the discrete GPU and use only the integrated Intel: https://apple.stackexchange.com/questions/166876/macbook-pro...
It is definitely GPU + heat related, but disabling the GPU is an unacceptable solution. People paid top dollar for a Macbook Pro with a fast GPU, you don't tell them to write off the premium they paid for that feature by disabling it.
But here's what the real problem was. Apple pretended the problem didn't exist for a very long time.
There was a huge thread on the Apple Support site related to this issue that was literally hundreds of pages long that spanned over a year. People were resorting to baking their logic boards in an oven to fix the issue, albeit temporarily.
Many people eventually gave up and wrote off the hardware before Apple finally acknowledged the issue with a repair order. This happened to me. I had the logic board replaced once already while under AppleCare (and the issue came back a few months later, but there was no point in constantly having the logic board replaced with another having the same design flaw). Just before my Applecare lapsed, it died. I wasn't going to pay $500+CAD for another defective board.
I was lucky I kept my unit around long enough when the repair order (recall) was issued. It still ended up dying a while later.
Apple had many options to make their affected users whole. They make enough money that they could have replaced everyone's 2011 model with a 2012 model (even a refurb would have been OK) which had none of those issues. Had they done that, I'd probably still be a Mac user (using that very same 2012 model) right now.
In the end, that experience completely soured me from Apple.
It's amazing Nvidia got away with their scam GPUs and didn't go bankrupt from their intentional underreporting of GPU thermals / power consumption that led to the mess.