It's been a while now since my last reply and I want to report that this stability issue no longer occurs. The thing is, I'm not sure what actually caused the problem to go away. I applied your solution on the other thread that you pointed me to, and it seemed to improve system stability by quite a bit although not entirely getting rid of the problem. I then made the mainboard's sensors work under Mint (it didn't work out of the box) and now I no longer have any kind of annoying random freeze any more. Thus, I think the solution you gave me plus functional mainboard sensors under Mint have sorted out the stability issue for me. But well, that's simply a wild guess at best unless somebody could say otherwise.
Thank you for your help. I owe you quite some.