High CPU RPM when GPU mining

Just got my MSI R9 280x couple days ago and decided to give this mining business a try. Everything seems to work great but my CPU fan (AMD FX-8350) is spinning a lot faster than usual (4k+ RPM vs 2.5k on idle). I only mine with my GPU. Sure I have observed a +3-4 deg C (36 to 40) rise in temperature of my CPU surely due to the graphics card working but would it explain a 75% bump in fan speed?

Does leaving it as is could damage my computer in the long run and should I consider a beefier solution for cooling (i am running the stock cooler).

What are you using to control your fans? There must be something that ramps up your fan when it senses other components getting hot, or maybe you have a temperature target of ~40C in your bios/fan control software. 

I tried using speed fan but couldn't get it to go any lower (only faster). Didn't check my bios. Will do and report back.

If the fan on your GPU is not a blower it's blowing almost all the hot air into the case, heating up the heatsink and processor causing it to ramp up. You shouldn't need anything more than the stock cooler unless the noise annoys you or you plan to overclock. As for the fan speed it's most likely the fan profile used in the bios and you may be able to adjust it through software.