Thanks I didn't know. Also my apologies. I thought I wrote a reply but apparently it didn't go through.
I use a MSI P55-GD65 (MS-7583) motherboard. This morning I had the black screen again, but everything on my computer was using default clocks. I removed the fan and that seemed to fix the issue. Haven't had problems since then. Overall I'm very confused. Not sure whether to replace my mobo or my PSU. I doubt the CPU fan itself is the cause of the instability, but I'm not that much of an expert so who knows. The PSU was fairly expensive (~140 euros with tax I think). A new motherboard would mean I would have to reassemble the whole computer, and that will probably only lead to more issues knowing my skill with tinkering.
I might buy a cheap tool that can measure the power that my computer is consuming. Not sure how hard it is to apply that though.