Both programs can, and will, use all of your CPU power at times. In Civ3, for example, the game will use 100% of your CPU power while it calculates the AI turns - which can be several minutes if you've got a lot of civs on a very large, well-developed map, and will be at least a couple minutes even on the fastest processor you can buy. But while it's your turn it will use very little CPU power. Alpha Centauri, on the other hand, may use 100% of the CPU power even when it is not your turn. Thus, while Civ3 allows it to cool down before maxing it out again (at least on the size of maps you're playing - try 200x200 and 31 civs and it might cause overheating, too), Alpha Centuari may just max it until it's too much. Run Task Manager while the game is up to see - if Alpha Centauri always uses 100% of CPU (50% if you have dual-core), then it is causing a much higher risk of overheating than Civ.
Games not using 100% of CPU power is one of the advances that has increased efficiency. Back in the days of DOS 6.22, even the operating system always used up 100% of the CPU all the time (and it still will use 100% if you install it on a new computer with new hardware), so efficiency and overheating-wise, DOS 6.22 is worse than even the most demanding new game.
At any rate, your processor should be able to handle 100% CPU for hours at a time without overheating provided you don't live in a very hot area. I'd suggest dusting your computer if you haven't lately, and if it's a laptop perhaps buying a notebook cooler. They're supposed to reduce temperatures, though I don't know from personal experience how effective they are.
Also ought to check and see if there are any non-functional fans. That's a common culprit in overheating.
