Seeing as they're nearly the same price, I'd go for the GTX 470 if your PSU can handle it. Yes, the card runs hot but most designs blow hot air out of the case so high temperatures aren't too much of a problem, i.e., the GPU will run hot but it won't affect other component temperatures much, if at all, either.
Note that the fan can be quite loud at > 60 % or so from what I've heard with the GTX 470, so if noise is a major concern then you'd be better off with the HD 5850.
^Now you know and knowing is half the battle. GI JOE!. This Forum is heavily monitored, which is why I like it so much. It keeps the real riffraff out. The George Burns Monkey is a good man. He is just keeping the natives in line. haha.
What does the rest of your system look like? What power supply do you have? That case and cooling setup do you have? Sure the GTX470 runs hot, but it is something we all have to just accepts. It is a powerful card and does alot of things, its a large GPU. I think if I would be installing a 470, I'd probably add an extra fan or two just for good measure to ensure it is cool. That probably isn't needed, but I'm weird like that. I still think I'd take that card over a 5850 if the prices were the same, which they are right now.