Low FPS after long time pc is ON, settings doesnt metter

Aug 15, 2018
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Let's start from the beggining.
I turned my computer on, playing League of Legends on 300-400 FPS - the highest possible settings. I played for about 2 hours, then started using Facebook and YouTube in the meantime, and after 6-7 hours while my PC was still working, I got to the game and suddenly the game started working on 40-45 FPS, hour later it was 30-35, followed by 15-20 FPS in the end.
For unknown reason only PC’s restart helps but there is another problem, it takes about 10-15 minutes to start working. (Shutting down and turning on again takes about 30 seconds but it doesnt solve my problem with performance in the game).
Thank you in advance for any ideas how to solve this issue!

GTX 960
Intel I5 4590s 3GHz
Windows 10
SSD Goodram cx100
 
Solution
I would be running some diagnostics just to be on the safe side-try memtest86 or even window's own memory testing tool. Also what are your temps when your system starts to slow down?