The stock cooler is designed for running stock, even in a poorly ventilated case, so you should have no problem assuming your case has some ventilation. The only concern I'd have would be noise. I know the 4870 heatsink is noisy and I believe it is the same one for the 4890 so you might want to get an aftermarket heatsink just to cut down on the noise, but temperature wise, you'll be fine.
__________________ Project: Black and White i7 920 D0 | 3 x 2GB DDR3 | EVGA X58 SLI LE
XFX 4890 | Corsair HX750 | Corsair Obsidian |