Yesterday while playing AC2 the game was constantly shutting itself down when I am in a battle with large no of templars!!! Is this a bug?? My system is not overheating, Asus pc probe 2 temps(CPU 44C, GPU 50C, MB 36C, HDD 35C).
Is it only happening with ASC2 or also with other games? Maybe you can try to run 3D Mark Demo to check if it will run ok. If the test for 3d mark will pass, than its no hardware but software. You could try to reinstall your game afterall.
Did you tried to reinstall? Just make sure you put your save games on a safe place. After you uninstalled the game remove also the folders for assassins screed on your harddrive. Also make sure you go to my documents and remove all the files for AS2. Go to start and enter in search bar "folder options" than go to tab view and choose "show hidden files, folders or drives" apply. Now go to your start menu again and copy the following string in your clipboard: %AppData%
This will show you some folders and search for everything that is bound with assassins screed 2. Remove the folders for as2.
Run CC cleaner http://www.piriform.com/ccleaner
Use the cleaner option and do this also for registry. registry will clear faulty registers.