Yes. This is 100% a heat issue. Crysis stresses your card in ways that no other game even comes close to doing. You'll find every game will run fine, but Crysis will freeze after 10-15 minutes. There's no driver update that will fix it. It's not a software crash. It's simply that the card gets too hot and malfunctions causing the freeze and reboot.
It's been very well known about in the Windows world for a while now especially with 8800 series cards. The only real solution is as follows:
1. Install RivaTuner - it allows you to monitor the core and ambient temperature of the card as well as set fan speeds.
Download here:
http://downloads.guru3d.com/download.php?det=163
2. Set the fan speed to 100% (maximum cooling) during gameplay - sorry it's a bit noisy at this speed, but it's either that or fry the card - and it's still quieter than the Radeon. Wear headphones if it annoys you.
3. Run the game in windowed mode so that you can adjust the graphics settings until the temperature stays more or less even. Some in-game effects (e.g. a lot of water) will stress the card more than others. Try not to let the card go above about 65 degrees - that's when you're getting close to freeze territory. 50-60 degrees is ok.
Be aware that fullscreen mode also causes a lot more heat than Windowed mode. If you want to figure out your settings for fullscreen, you'll have to alt-tab every couple of minutes to go back to the desktop and check the temperature until you're sure you have stable settings. If you can bear to have the game in a Window - do it. It's a lot easier to watch the temperature and you'll notice immediately when it starts to rise. I've been able to have 3-4 hour game sessions without a freeze by doing this. If I just launch the game without taking these measures, it dies after 10 minutes.
Be warned Crysis can make your card temperature rise at about 1 degree per second! No single game is worth taking chances on damaging your hardware. Get yourself setup properly first at whatever settings your system can bear, and then enjoy the game.
The alternative is to install a 3rd party cooling system. For that you're on your own.