Very weird frame rate ups and downs

When I play heavy games like Rust I usually play with a poor fps, rarely more than 20. Yet sometimes it randomly goes up to 30-40 for a minute or so. Today I tried to tweak some settings in the Radeon Settings panel and I noticed that when I changed my Texture Filtering Quality to "Performance"  the frame rate instantly gone up to 30-40, but again for about a minute. Then I tried to test how bad it would run if I changed it back to Standard and I even changed the RustClient.exe to "Power saving" mode in the Switchable Graphics menu only to find out all those tweaks make no difference to my frame rate now - it stays 15-20 no matter what I tweak. I know that Rust is a poorly optimised game, but the same weird stuff happened today with Fallout 4 too - the frame rate was low, I changed Fallout4.exe to High Performance in the Switchable Graphics and then my frame rate improved for just a minute before going down to 15-20 again. Any help on this case would be much appriciated.

 

My PC specs are as follows:

 

8GB DDR3 RAM

Graphics Chipset

AMD Radeon(TM) R6 Graphics

AMD Radeon R7 M260

CPU Type

AMD A10-7300 Radeon R6, 10 Compute Cores 4C+6G

Radeon Software Version

17.7.2

 

It runs Windows 7 Ultimate x64