FPS Drop After The 9 Minute Mark.

I've been having issues with FPS skips around the 9 minute mark. I've talked to a Riot Tech Support named c4rs0n who was very insightful, and submitted a ticket, but unfortunately I'm still having the same issues. What I was told to do was uninstall my current drivers on my GPU then reinstall a more up to date version. I've also tried using the hextech repairtool to see if I had any sort of corruptions, and even tried uninstalling and reinstalling. I didn't start experiencing these drops until the hotfix that happened not to long ago. I would usually play the game at 200fps easily, but when the 9 minute mark comes around my FPS gets around 10-20 FPS. If anyone has some suggestions as to fix the issue I would be very grateful!