Traizlover, one obvious question is "what is the ambient temperature in the room where your PC is?" If it was 75 degrees F it would mean your PC would never be less than that temperature and would struggle to stay cool.
Regarding the CPU and Heat Sink, think long and hard before you touch them.
I had the same problem you did (PC cutting out when I played Far Cry) and on looking inside I found the fan and indeed the whole PC - which I had for 2.5 years - was full of dust. I dismantle the fan/heat sink and found the sink was packed with dust almost like cotton wool. I cleaned and reassembled them and everything seemed to work fine.However I checked things by shutting the PC down and then powering up and going into BIOS to check the heat.It was alarmingly high,so I ran the PC with the side off and found that the CPU fan wasn't spinning. I removed it and tested it on a 9 volt battery and it ran fine.
I searched on Computerhope.com and was advised that the Speed Sensor on the fan was probably fried.
I then bought a replacement fan (about £15 UK) and fitted it.It didn't move.
I left the PC for about 6 months as I had simply got tired of trying to repair it. Finally I did more searching and on another forum found the probable cause of the problem - when I cleaned the fan I had to unplug it from the motherboard and it seems likely I disturbed the soldered joint, hence the fan was getting no power! :'(