It would be a rare thing - a defective plug - all new machines in the UK come with a moulded on plug these days.
A plug should not get hot under normal operation with normal current flow. If the current flow were too high a fuse would blow and you have no fuse blowing. The socket is new - the new one may aslo be defective (dirty connector) - Inspect the prong ends of the plug for the stains of sparking.
If it were mine I would just cut the plug off and stick a new one on but you have the machine's warranty to consider. You may do well to make a claim before there's a fire.
A plastic plug on a 3kW fan heater for instance will get warm with the normal current flow and need to be replaced in time especially if run for long periods - the hard plastic breaks down chemically.
I cant see the plug on a new appliance becoming warm unless the plug itself has a manufacturing defect.
If you are in the USA the voltage is half but the current is double - this makes the heating from a dirty connection more acute becuase of the current squared thing. 1 Ohm resistance connection to a 3kW appliance in the US is 680W !!!
Good luck...
Peccavi
February 2010