Well if you had to make a warranty claim, they 'might' but it's unlikely. I have had a lot of cpu's over the years, and the only one to ever actually stop working on me, was entirely my own fault, back in the old AMD socket A days, I cracked the core on a Duron when reseating the HSF unit as AMD thought it was a brilliant idea to not bother with heat-spreaders, which also protect the cpu then.
I really wouldn't worry about it, besides the one in your signature is really cheap, people will buy those in multiples just to see how much speed they can ring out of it, while I'm not suggesting you do that, I'm simply saying, as far as cpu's go, the Athlon X2 240 is virtually semi-disposable. They very rarely go wrong anyway, it's almost never the cpu that gives up the ghost, unless you are pumping a lot of voltage beyond the recommended into it over a period of time. If you are running it at stock voltage or close to, it'll go on working well beyond it's useful life.
As I say, not worth worrying about really.
