You should have followed my link for one for £110, that I put in your thread
The CPU will be fine, Intel has superb thermal protection.
Basically Prime95 throws difficult calculations at the CPU, if there is any problem with it, Prime will tell you that one of the cores has errored. Chances are, that if your temps are fine now (have you checked?) then it will be fine
Your tip was much appreciated! I just wasn't too keen on buying one secondhand - and I think the £110 one was a second hand one on Ebay? I'm sure it would've been fine - but I wanted to minimise chances of component faults as this is my first bit of PC tinkering!
CPU temperatures - how do most people monitor CPU temperatures? Is there a popular program for this?
Since I installed the screw-on cooler with some thermal paste, the PC no longer randomly shuts down. Also, the fan seems to run quietly and when I put my hand next to it (the CPU fan) it doesn't seem to give off much, if any, heat - so I'm assuming that's a good sign?