Yes, the 4870X2 and 5970 run extremely hot.
Hell, I have a 4890 that idles at 60c.
However, these single GPU 480s are the hottest single GPUs I have seen. Enough to make note of I think.
Either way you're both right!
Much can be argued about both.
The 5970 is going to have better heat&power to performance ratio along with price.
However the GTX 480 has shown to have extreme scaling abilities (up to 89% if I remember right). And, like it or not, GTX 480 tri sli is the strongest setup available.