It could be heat or power related. Since you say that power supply is old it may not be delivering the power you need under load anymore. You can test if it drops below 12v with a free utility called OCCT from ocbase dot com.
If that test has all components pass I would try raising the "Power Limit" slider in Radeon Settings to its maximum and see if that helps. The slider is in Radeon Settings / Performance / Tuning. Just slide it all the way to the right.
If the issue is heat related you can try a more aggressive fan curve also in Radeon Settings that kicks the fans up higher sooner.
Was this always an issue or did it just start recently, or after a driver update?
If it only happens in just this one game it just could be you need to tweak some in game settings.
This is a pretty good optimization guide for that game:
https://esportsjunkie.com/2018/03/28/best-csgo-settings-optimization-guide-2018-samiz1337