Removed the outlet and the three connected neutral wires were insanely hot. Have an extension cord running a heater, could it be the draw or do I just need a new outlet?
No, normal heating will not scorch the insulation and certainly won't make an glowing connection. I'd definitely disconnect that space heater before a fire starts and you probably ought to turn off that breaker to be safe. Get it checked out, it could be nothing more than a loose connection, it could be something more complicated.