Wrap your 360 in a blanket or a couple towels. Make sure it is fully covered, especially the fan area. The idea is to overheat your xbox. Wrap it up and turn it on for 15-20 minutes. It might shut itself off a time or two so know where the power button is under the blanket/towel.
After about 15 min unwrap it, let it cool and turn on. It shoudl be working. This is known as the towel trick and there are youtube videos explaining it in more detail.
This is a shortcut, the proper way of heating your xbox really is a heat gun. Once again look up the heat gun fix tricks on youtube or google. You may have to do this every once in awhile to keep the xbox going.
Tim, April 2008