You mean Microsoft? A lot of the time they just exchange your XBOX with a refurbished one, so the problem usually shows up after time once again. If they repair it, I assume they replace the clamps or something, which would still cause the console to die eventually.
There's a fix on the internet which has had a high rate of success, the X-clamps replacement fix. You remove the X-clamps holding the CPU/GPU and replace them with screws/nuts (while adding new thermal paste to the chips).
I actually bought a broken 360 off ebay with the 3ROL and used the fix to revive it. The fix is only a few months old so we'll see the longevity of the method over time.