Yes, That's your solution Brendan
A few of the reasons Playstations and Xbox's overheat is because they get full of dust of course, and the manufacturers use very cheap Thermal Compound. And the constant heat from restrictive dust or the failing Thermal Compound weakens the solder joints under the CPU and GPU. You can probably save your system by:
If your comfortable in doing so and not worried about the warranty..
-First, Order some Arctic 5 Thermal Compound from here..I use Noctua NT-H1 Because it does not solidify or have the supposed break-in time. I don't recommend the RROD Bolt kit, but it already comes with Thermal Compound.
-Make sure your grounded or at least touch something metal as your going through the process. ESD can be bad..
- Tear it down and clean it as you go. Replace the thermal compound.
- If you don't use the bolt kit, Just give the X Clamps a slight bend before you re install them.
- You can also try to relow it yourself. I don't know how successful it is using a heat gun because I have a BGA Machine...Worth a try though.
-If you get it up and running, Clean it at least once a year and keep it where it can breathe. If your a Heavy Gamer..I would clean it every 6 months and change the Thermal Compound every year.
This is just some cheap suggestions that might get you up and running again before taking it to a shop to have it reflowed "Witch is what Microsoft would do if you send it to them anyway", but takes forever for it to go through the process.
Hope this helps....