I have an older Delongi Oil filler radiator and the plug burned up because the outlet was not making good contact (Older GFCI, Which I will replace also)

Both the plug and receptacle were noticeably melted on the hot side (However the GFI did not trip and when I pushed the test button now it just buzzes and will now trip the breaker in the 20A kitchen circuit) Anyway is there any tips on how to replace the cord cap on the heater? The heater wire is the high temperature 16 Gauge x 2 conductors and is not grounded

Is there a special way to terminate the cord cap or even a special part brand or model number that I should use? All I can find for heavy duty cord caps are the grounding style which I assume I can't use as the heater has no grounding wire

PS: I don't want to throw out the heater as it still works and it is not one of the ones that are made in China (Made in England) so I rather keep it (Plus it was an expensive heater)

PPS:

The heating system in my house is fine I just use it so I don't have to keep the thermostat so high to save a few $

Thanks