Computer stuff always gets hotter the harder it works, it's just that you notice it more with a laptop because it's on your lap and there's not much room for a cooling solution in there. Doesn't mean it'll fry though, it might just be less comfortable. "Gaming" laptops are typically an expensive variety, you'll pay more than you would for the same performance on a desktop system.
Just look for something with discreet graphics processing as opposed to integrated video. The "GeForce M" and "Mobility Radeon" are Nvidia and ATI's line of cards, respectively. The higher the model number, the better, pretty much. You can see some stats and benchmarks here.
You could get a desktop put together that would blow through those games and more for 500-600, but I'm not quite as confident about getting a comparable notebook in the same price bracket. I don't know what those games actually require to run well, though, so maybe it won't be a problem.
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