Shutdown problem!!?

Hey guys, I read alot that the newest macbook problem was they heatsync is dumb. Anyway, mine just started to shutdown by itself yesterday (i've had my macbook when it first came out).

So my question is this. I have another macbook but i need my HD cause i have alot of work to do and alot of what i need is on this hard drive. Can I just give the apple store my laptop without the HD in it? Or do they need the whole thing?

Thanks!