Well - assuming that speedfan isn't broke:
It's very possible that you haven't connected it properly (the heat sink isn't close enough to the CPU), or applied your thermal paste incorrectly. - You want a pea-sized bit of paste, and squish the paste down with the heat sink, so it spreads out in between any of the gaps, which it's supposed to cover.
>The thermal paste is only supposed to cover parts where there would be air between the heat sink and the CPU<
This is image is roughly what a close up picture of thermal paste does for a heatsink and CPU:
Unfortunately, I couldn't find the picture I wanted to show.
The red line is the ideal straight, the green and blue is the paste, and the jaggedy black lines is the actual surfaces of the CPU and the heatsink. As it's quite hard to get a perfectly straight CPU and Heatsink plate, you use thermal paste.
You can ofc lap the heat sink, (and even make it reflect light like a mirror) - This one is fairly well done:
image. Although you shouldn't lap the CPU, for obvious reasons
Anyways, the TIM is just to cover any gaps (the paste is more conductive than air), not to smother the CPU (less conductive than bare CPU/heatsink).
When your specs far outweigh the game and it's still locking up, it tends to be:
Heat (possibly not, if it is actually 30*~C)
Hard drive - Assuming it's not nearing its maximum capacity; (You can check it with
Crystal Disk Info)
Software/Drivers - They are generally to do with the GPU in games, although other drivers can affect a games performance.
Hardware failure - Possibly the PSU not being able to deal with the stress that the GPU and CPU are causing, when they both need to work hard to render games. (Although the make and model seem fair, you may be unlucky, or a cable is loose).
Although other people have said some of these points, I thought I'd reaffirm them, and possibly add some things which haven't been mentioned before.