When my 5870 started doing that, the fan had finally given up. I just took the HS off and pointed a few 120 mm fans at it.
Problem with the 5970 is that the entire thing needs to be taken off to remove the plastic shroud over the heat sink. Depending if I have to ship this thing to Hong Kong or not (That is where HIS are based) I may just opt for water cooling...even if it is just this one card for now.