Can I use a can of compressed air to rid my Xbox 360 of overheating problems?

I’ve had my Xbox 360 since launch and have had nothing but trouble. I’ve had to send it in 3 times to Microsoft already (red rings twice and a faulty disk drive) and by now my warranty has long since expired.

Now I’ve been getting two red rings which apparently means it’s overheated. I can’t afford to buy a new Xbox so I was considering taking it apart and spraying the insides with compressed air to remove the dust. I was wondering if this was a good idea and if it will help fix the problem. Also, do I have to take it apart? Can I just spray inside the holes on the back without actually dissecting my Xbox?