If the installation is correct then worst case should be a blown fuse. However we all should have our houses checked every ten years or change of occupant and one of the tests is that the ring main is a ring. If not then one could load up 32A on to wiring only rated at 20A approx.
Also 3Kw is max for 13A plug and if like the kettle the fire only runs for 15 mins then switches off on thermostat then no problems but where the fire is one for hours then the plugs can over heat.
But in real terms the biggest problem with electric fires is items being placed on top of them. After a fire while working for Laing we changed all our convector heaters for oil filled radiators as they were less likely to set paper alight. So easy for draft from door to set papers floating.
Most fires are due to some fault with the fire. Thermostat not working. Or thermal fuse shorted out. And while attended not really a problem.
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