Play in a freezer
Playing your 360 while keeping the system in a freezer seems to be the only logical answer. I suggest buying a mini freezer to place next to your entertainment center and keeping your 360 in there 24-7. Otherwise, utilize the warranty and then sell it on e-bay. Based on statistics, even if you get a working one back, it will break again after the warranty is over. Sell the replaced working unit while it's worth something and then buy a PS3 and/or Wii.