Your question is in the Coffee Machines category but no matter...
It might be a poor connection somewhere - in the plug itself or even in the socket you plug it into.
Try in an alternative socket outlet & consider chopping the plug off and fitting a new one.
If you can - inspect all terminal joints for cleanliness and security - check the plug's pins are clean and bright.
Your appliance probably takes a high current - and a slightly high resistance connection with a high current will generate more heat than a lightbulb - this may well be what's heating the plug.
Peccavi, June 2011