Oh, F me, who fitted that plug???
that plug has been fitted wrong and is quite dangerous.
The wires should be tucked around the little lugs that form a cable restraint - to stop the wires pulling out if the cord is yanked.
You can see a tiny slot in the base halfway between the pins in photo 1, there will be a protruding plastic lug above each slot and the wires should be threaded around the lug.
How many amps does it draw? Standard Australian plugs are only good for 10 amps, European appliances often draw 13 or 15 amps, this is enough to burn out an Australian plug if there is any imperfection in the connection.
The more I look at that wiring, the more I think you should cut off the cord and keep the heater as a curiosity, not a working heater. It is so far from a safe design it is ridiculous. The insulation is rudimentary, the cord anchorage is terrible and non-compliant, and it should be earthed.
If you ignore my advice and repair the heater, at the very least get a moulded in one plug and cord, and use one made for high temperature devices. Standard flex would melt inside that heater. High temp cords have a different feel, more rubbery than plasticky. (But they aren't rubber, to be clear.) The cable often has "High Temperature" or a numerical temperature rating printed along its length.
But please don't. That device is inherently unsafe.
If you burn the house down, you would probably be uninsured as that heater doesn't comply with Australian codes, even those from decades ago. And you or someone else might end up dead.
