Dunno what the stock Intel coolers are like, but if you're worried about heat, it's nothing a decent aftermarket cooler wouldn't solve.
As said, there's not a lot between Red and Green atm, but if you choose Nvidia, go for a 6-series card.
@Kelmola: Maybe your fan died...
What to replace it with depends...if you're buying new, you don't want to part with your cash and see no improvement, so I'd go for the 7870, esp. if you're able to upgrade the CPU (if needed) on that particular motherboard.
But if you're planning on a full rebuild anytime soon, I'd just go for a second-hand equivalent.
Wanna buy a slighty used 5770?...