Remounting the cooler can correct the possibility of the original mount being done in such a way so that the bottom of the heat sink is not making good contact with the top of the CPU. Screws not tightened evenly, cooler wedged against another component in the case, TIM not being applied properly, etc. If you choose to do this, carefully separate the cooler from the CPU and examine the spread pattern of the TIM. If done correctly, it should show coverage across the entire lid of the CPU if it was done correctly.
But first clean the old stuff off with a coffee filter moistened with high concentration isopropyl alcohol. I use 91% when I can find it. Less water in it than 70%. Coffee filters have no lotion like a lot of facial tissues and have a hard sheen which doesn't leave so many fibers behind that can insulate. Reapply the TIM with a pea-sized glob in the center. Don't try to spread it. Let the clamping pressure do that. Tighten the screws back and forth a little at a time to make sure pressure is even during the mount. Like tightening automobile cylinder head bolts after replacing the gasket.
But the question I want to ask is what is your case ventilation like? How many intake (bringing air into the case) and exhaust (extracting air from the case) fans do you have? Where are they located and how big are they? High temps can be caused by poor case ventilation. This can be tested as an issue by removing the side panel off the case and running the stress test again.
Also, please create a Sig listing your components in some detail. Go to the top of the page and click on Settings and look down the left side. You will see "Edit Signature." You can refer to my sig if you want a pattern for what we look for.