Yeah, that really sounds like a heat issue.
Have you been making data backups? You have, right? Religiously? What am I saying—of course you have!
You want to open the case up and blow it out. While you can certainly blow a little air into the vents and see puffs of dust escape, a lot of debris will be trapped, as long as the case is closed up.
If you're not comfortable doing this, have someone else do it.
I bet that will stop the issue.