I have noticed that My HTPC system that has become my main system of late is running hot when I play CH. Its an AMD 8A-5600 with 4 gig of ram. I'm running 'windows 7 64bit, without a video card may look into that part. This only based on the fact the fan tends to run at near max speed when in a game for more then 5-10 minutes. I would not expect a browser game to make this system run so hot. Just putting it out there, in case someone may know of a way around this.
Flash isn't a very light game engine sadly, usually related to that rather than the specific game in itself - think it relies more on ram and cpu than on graphic cards.
If you get problems the longer you play consider trying a different browser as they handle flash and memory strangely different.
Its not so much a problem it just makes the CPU fan run fast and that gets loud, I will try some other browsers. Trying Chrome when the server comes back.
My primary machine I play on right now is my Mid-2011 Mac Mini with just 2GB of memory (also driving a 55" screen). So far I haven't seen many issues, aside from a few odd network hiccups possibly more related to electrical storms than hardware. It's the same machine we used to demo the game, with a smaller screen, at SXSW back in March.