Very hot live pin on kettle plug
You forgot to mention the type of plug but your user profile says UK so it's a 13 A plug.

Figure 1. Photo by Pfnicholls at WikiMedia commons.
The L pin runs warmer than the others due to the heat generated by the (low) resistance of the built-in fuse and, possibly, the fuse contacts.
If you're concerned then replace the kettle lead or, if you know what you're doing, you can cut the plug off and use a rewireable type.

According to The Art of Sound forum the 13 A fuse resistance is in the order of 10 mΩ.

Your 2 kW kettle will draw \$ I = \frac P V = \frac {2000}{230} = 8.7 \ \text A \$.

The heat dissipated in the fuse will be given by \$ P = I^2R = 8.7^2 \times 10m = 0.75 \ \text W \$. In normal practice this should be conducted away by the terminals and wiring. The fact that it is not suggest that a lot more power is being dissipated and this is most likely due to poor contact somewhere.


You could try removing the fuse and pinching the contacts together before reinserting the fuse. The extra &quot;bite&quot; may lower the contact resistance.