If your machine is cutting out the first thing to check is your filters if these are not clean the machine will cut out but it is more likely that the cyclone top needs replaced Dyson did a modification on this a few years ago, you can not buy a thermal cut on its own they would only sell you a new motor they would also not recomend that you repaired it yourself.
Try one of the links on this page they may sell you the part, the cut out is mounted on the motor so be carefull and good luck.
Gary McDonald, March 2006