Randomly shuts off after about 10 minutes.

MacBook Core 2 Duo mid 2007

I tried the firmware update. It says I don't need an update. Maybe this is because I've got a Lion OS on it.

I've tried taking it apart and vacuuming all the dust out. I put it back together and everything works just as it did before. Maybe it's an overheating issue? It does get quite warm.

As far as I know there is no water damage or anything like that. It has a ton of software on it and was low on space. I deleted a lot of photos and videos to make room in case it was a storage issue.

Also, the battery pack died on it about a year ago so I just plug it straight into the wall. Any ideas?

Thanks in advance!

Nicole