Just to state evga precison is only for nvidia cards. Hence why it says this.
http://www.evga.com said:
EVGA 6, 7, 8, 9, 200, 400 or 500 series graphics card, Forceware 96.xx or higher drivers
You wont need to worry if the card gets to hot it has safeguards to stop it over heating, max operating temp is 100 to 105c, although you want to be a good amount lower than that, like say at least 10 c lower, if it does get to high i should under clock itself to lower the the temp.
Have a look here you will see the temps techpowerup had when using their hd5870
http://www.techpowerup.com/reviews/ATI/Radeon_HD_5870/33.html
I leave my HD4670 fan speed on auto and it does the trick fine, Id say bump the fan speed to 45% at least or when you game enable the automatic mode.
If you want to bench it and see how high the temps are use occt.
I have used all of the other tools, msi kombuster, ati tool, furmark etc and none of them stress my gpu as much as it that does, on all other benchmark programs, with all settings on max, my gpu will have a max temp of around 65c and with oc it showed no artifacts.
On OCCT with all settings on max and error check on my gpu temp goes to around 85c, it doenst even go that high whilst gaming for hours, it is also the only way i found out my gpu was artifacting at the temps I had, and I think that was probably what was causing my pc to crash whilst gaming.
http://www.ocbase.com/perestroika_en/