I would like to check some additional information on this.
Have you monitored what is the temperature values you see in the system BIOS?
Also what is the temperature of the processor when you see that the system crashes?
What specific tasks or applications are being used to trigger this issue?
Are you able to easily replicate the problem or it happens randomly?
By now, you should have the latest BIOS and drivers for that motherboard and hardware, and also test using less memory in the system too, trying to check if the crash is not related to memory problems. Over heating causes the system to shut down completely, in which the system should stay off, so those restart issues may be related to other hardware in the system.
You may also check for a replacement on the processor if its a boxed unit, using this contact information:
BIOS says 44C when I turn on the computer.
The BSOD mostly happens while playing video games, like CS:GO. It crashes at least once every 30 mins. The reported temperature in Open Hardware Monitor for the CPU package is around 70C I think. I will check again later to see what exactly is going on.
I tried memtest86 and passed after running it for several hours. I also bought a new video card/PSU and that hasn't made the problems go away either.
Some people suggest I reapply thermal paste on the i5. Will that void the warranty?
Applying more Thermal Interface Material to the processor does not void the warranty of the processor, so, you can go ahead and try that. Also clean the Heat Sink to make sure that there is no dust preventing proper airflow through the Heat Sink. Update the system BIOS.
BIOS is up to date. Heat sink is also very clean. I cleaned and reapplied thermal paste right now. It doesn't appear to have changed anything and there is no difference in temperature, but I will wait until tomorrow to see. How does the RMA process work? I need to use my computer for work so I don't want any downtime.