Had the same prob as you do.
First check with system settings to see if xbox is actually overheating.
If you open the case, the xbox should not overheat.
My xbox was not overheating and I knew the modchip was ok, so I ordered
a new psu from Lik-Sang. And guess what, everything was working after that
I have a 1.4 xbox and it seems like the original psu's are not quality products.
Just by comparing with the original and the new you can see the differences.
The new has protected shields and none of that white shit on the card.