install some temperature monitoring software like HWmonitor and GPUz, just search for them, they're free.
Use that to check temperatures, its possible that the R7 is running without problems and something else is making the smell.
I've noticed that amd videocards from R7 to current generation dont turn on fans until you start gaming.
My R7 360 fan doesnt spin when im just browsing the internet.
Update us with your temperature while idle and while gaming, then we can...