Heating of 13 Ampere Domestic Plug Pins - second opinion needed.

I have a heater plug warming up on an 1800 Watt ceramic fan heater and carried out the following checks to see if I could resolve the matter. The cable is only warm at the plug:

a. Plug checked; it is wired correctly and so in good assembly order.
b. Wire strands have been soldered at the plug-pin termination.
c. Plug changed for an MK one and the heating effect was still noticeable.
d. Resistance measurements using my multimeter on the lowest (600 Ohms) range. The readings for the plug (pin-to-pin shorted; and individual plug components, including the 10 Amp fuse) were below 0.1 Ohms. These readings are the same for the MK plug.
e. During the resistance checks I wiggled the cable close to the plug to see if there was an internal cable fracture, with no changes in the resistance being observed.
f. Using my multimeter, I measured the temperature of the plug pins when cold and after running for a period (about 20 minutes) and measured an ambient temperature of about 20 degrees C, and so similar temperature for the plug pins when cold. After the 20-minute run, plug pins were about 35 degrees C. I did this temperature check using two sockets in different rooms, one of which has only been fitted for about ten years and is only occasionally used; also another socket on the upstairs ring main. So sockets are eliminated.

Opinions most welcome.