Hi we just had the same problem. It will be one of two things:
1) check + wash or renew filters (leave for good 24 hours to dry out properly). Remove the dustbin and swish around in hot bath water over and over .... dry out properly afterwards. (The motor tries to suck cold air down through the dustbin - a blockage will cause your overheating problem).
2) We tried the above and still had the same problem as you, turned out it was the thermo cut out on the actual motor. This protects the motor from catching fire when things get too hot. Some people bodge fix the thing by bypassing it - I advise not. You can't buy the thermo cut out on its own as its attached to the motor. Dyson will deliver a new motor for about £35 ... we bought ours on ebay for £25. Fitting is pretty straightforward with simple hand tools ... go to dysonmedic.com for a really cool idiots guide on how to fit!
Hope this helps
Keith
August 2008