You are square at the minimum configuration, maybe even below if your video card isn't 512mb.
The game could be laggy, but it shouldn't affect your PC once you quit the game.
In the troubleshooting guide above, try the part about reinstalling DirectX.
Also check the section:
III. Graphical issues
there's a file to download and copy in your game user directory, just follow the instructions.
I really think you should submit a support ticket with the link above and provide a full configuration info.
There is a tool to report hardware info I use, it's called HWinfo64:
Just run it, select "Report" from the menu and then "create". Select the HTML option, upload the file to Stardock on their support site, along with your prefs.ini, debug.err and save game files (c:\Users\My games\Galciv3 (or GC3crusade if you have it). They usually answer pretty quickly.
Maybe there's a leak that is only apparent on lower configs, it's a possibility. Even on an older system, once you quit the game, it shouldn't affect Windows like that.
Also, make sure there is nothing else running at the same time as your game.