The OP is trolling. There is no way the 7450 can run Skyrim like he is saying. Everyone on the internet have theirs running it at below medium, and still not at great framerates. Only way to get it to higher is to overclock. And, if grimmpickering is getting such good framerates, then he is overclocking far too high and taht is why his systems are dying on him. Plus with 10GB of RAM, you are not using equal DIMM/size sticks which is not a good thing when gaming. And if the rest of the system is this bad, it probably is not allocating the resources very well. The 7450 is a very bad card. It still uses DDR3 memory , and is not designed for gaming. The 8800GTS (which I have in an older machine) is far superior for gaming and ran Dragon Age perfectly.
Like goraththeelder said, software cannot damage a machine. There are safegaurds in place to prevent it from being damaged. It would shutdown once it got too hot. Unless you had a faulty machine, a game - no matter how bad it is - cannot harm it.
Sure, the engine in Dragon Age had it's problems. But, it is not what is braking your machine. Remember, Skyrim uses visual trickery to look as good as it does. Oblivion with mods is more demanding than that game. Comparing apples with oranges.
Please, Sir, don't be so nasty to people who were trying to help. You will get nasty responses back. Not everyone can afford super high end machines, that's fine. But, to go around trolling a game - when you have a machine that clearly is not very good - is not very clever.
TL;DR: The game won't damage your machine, provided your machine is not faulty/sub-par/over-clocked beyond reason.