Thanks for sharing your experience with the heater plug. That heater seems more trouble than it's worth.I have had the fuel heater plug melt on two different trucks and suck air through the plug. You can't see it melted until you unplug it. I filled the plug with silicone on one to get it home, and then removed the heater altogether once in the shop. The heater is not really ever needed. It about drove me crazy figuring this out, exact same symptoms yours has.
Can you elaborate on the description of the "plug"? Where is that located in the heater mechanism?
Looking forward to finding this plug!