Computer reboots when gaming without BSOD

Two things can instantly shut down without notice...either the power supply shut down due to detecting some error condition, or you had a triple hardware exception (https://en.wikipedia.org/wiki/Triple_fault).

In the case of heat this could explain either.

For a CPU, when it detects some errors it will run an error handler. Logging can occur. When there is an error within an error handler logging might still occur. When there is an error within this error, then the CPU is afraid to continue because everything is so badly scrambled it could destroy things and it is safer to just power off. Some issues with RAM could cause this even if the CPU is good...it just isn't common for RAM to cause a triple exception without something else showing up prior to reaching such a sad state. I tend to believe the power supply is a more likely issue, but I've seen both.

For RAM which is dual channel you may find each individual RAM stick works great by itself. If in single channel operation, then two sticks may still work fine together. When using multiple RAM sticks together you will often find they are configured to interleave...something like RAID0 where performance is boosted by reading or writing half of the content to each RAM at the same time. When the RAM goes multichannel and starts to interleave for performance you will find a single timing is used for all RAM sticks...the sticks must be matched and working together at that timing. If they differ in any way, but are otherwise working, you will still get failures. If your BIOS can turn off the interleave you might try that as a test with memtest86. Even RAM from the same manufacturer of the same model and same rating might differ slightly if not sold together as matching.

Someone also mentioned turning up the voltage on the RAM by a tiny amount...this can add stability (along with heat) at any timing. I would first try turning off interleave, and if this helps, you could try turning up the voltage as suggested and re-enable interleave.

Loosely related to this, and not necessarily likely, is that brownouts where voltage on the power line decreases by an amount too small to actually cause shutdown some voltages will drop slightly. One result is corrupted data in places like RAM. A brownout is somewhat analogous to purposely lowering RAM voltage. An UPS with brownout protection is very nice when testing for issues in a long test such as memtest86.

The CPU compound replacement was a very good idea. However, there may be other places where heat is still an issue, e.g., the power supply having dust in it. Or at high load levels the power supply just can't handle that much power continuously.

You might have a combination of problems as well.