Posssible faulty GFI receptacle

[TerryH]

A few days ago, while using a space heater drawing 12.5 Amps for 3-4 hours the interrupter on my rear vanity GFI tripped. The heater was the only load on that 15 Amp circuit, but not plugged into the GFI. The heater has a thermostat, so I didnââ,¬â,,¢t realize right away that it had tripped. When I realized there was no power to it I checked the breaker - fine, then the GFI - tripped -  and reset it. Half an hour later I checked the plug and cord of the heater and receptacle it was using to see if they were getting warm, as I regularly do when using a space heater. Plug was slightly warm as is common with these. Then I checked the GFI which I donââ,¬â,,¢t normally do and it was very hot. Turned off the heater and unplugged it. I tried the heater on the second 15 Amp circuit which was already loaded with the reefer and laptop, and then regularly checked each receptacle on the circuit for warmth - all were fine.
I removed the GFI and found the neutral Load wire insulation burned for 1 inch and a burn mark on the receptacle. Black wire (Load) and both Line wires were fine. I changed out the GFI and now check all receptacles on that circuit when it is in use. So far the heater plug still becomes slightly warm, its receptacle stays fine and the unused GFI receptacle  will occasionally feel a touch warm - just enough to feel.
This circuit powers the GFI receptacle (very rarely used and the only GFI) at the rear vanity, one at the galley counter (used regularly), one forward of the counter (used regularly and for the space heater) and one above the driver (TV, never used).
My question is can an unloaded GFI become hot enough to cause concern when the circuit is under load elsewhere? If so, am I correct in assuming that the fault is with the GFI receptacle?
I am ok with practical electrical work but at a loss when it comes to electrical theory.
Sorry for being long winded, but I am hoping to provide what info is needed.
Thanks

[Rickf1985]

Was the GFI feeding the other circuits? On a GFI outlet you have load in and load out to other circuits and they have to be set up in the right order. They are usually pretty well marked. I have never seen them get hot for any other reason than overloading and a loose connection. Are you sure the connections were good and solid? You don't have aluminum wire do you?

[TerryH]

No aluminum wiring, it was one of the things I checked before buying.
The GFI does feed the other three receptacles on this circuit. Load In and Line Out are correct. If they are reversed the Interrupter will trip, cutting power to all receptacles in this circuit.
All connections were tight.

[Rickf1985]

Sounds like there is just not enough contact area on the connections where the plug meets the contacts in the outlet. Chinese  quality?

[TerryH]

Sounds like there is just not enough contact area on the connections where the plug meets the contacts in the outlet. Chinese  quality?

Very much so. What I don't understand is why did the GFI heat up when the heater was plugged in elsewhere on the same circuit?

[tmsnyder]

Toasty!