Have you had a look inside the plug? Is it moulded on r the unscrewable kind? I have known the unscrewable kind get hot because wires are touching on the inside of the plug.
The plug getting hot means that there is too much resistance in the plug for the electrical current that it is carrying.The causes of the high resistance could be any or all of the following.
1. Fuse rating too low
2. Loose wire clamp screw or screws.
3. Broken strands of wire within the plug or where the cable exits the plug
4. An insufficient number of strands clamped to the pin.
5. Contact surfaces of the fuse holder oxidised or fuse not gripped tightly enough.
6. Contacts in the socket oxidised or not gripping the pin tightly enough.
7. Loose clamp screws in the socket.
6 & 7 above can be tested by trying the plug in another socket and by trying another appliance of similar wattage in the socket
Has this problem on my washing machine when I first installed it - changed the plug to one manufactured by MK - solved the problem - the MK plugs have a screw/washer type connection which is makes far better contact.