Im not a teckspert but if you have any problems try search what problems are occuring on a site and see if your problems relate to it, if not i would advise contacting microsoft support, also installing an additional fan or last of all trade it in for a new Xbox.
The whole 'cooling adapter' stuff isn't a good solution. You're better off moving the 360 to a better ventilated area (where air can get in and out of the 360 easily).
I used to have this problem when mine sat on the carpet, but now it's up off the ground and the issue doesn't occur.
make sure your xbox heat sink where the heat is comming out don't get cover by anything and the best place where you xbox don't get overheated is air con room.