I bought my 2013 Ford Fusion hybrid in July 2017 with almost 39,000 miles. I noticed the charger ring on the car did not light when plugged in using the charging unit that came with the car. Also the amount of miles in the battery after plugging it in at our house for 7 hours gradually diminished from about 24 miles down to 18 miles and a couple of times getting only 14 miles on that long of a charge. I scheduled a diagnostic with Ford.
Mostly the car would be plugged in about 7-8 hours. The outlet side plug was always extremely hot to the touch. I assumed it was drawing a lot of electricity so I unplugged it and replugged it daily. I took it my car to our only Ford Dealership. It took them a few months before getting a replacement charging ring- Dec of 2017, but they haven't been able to install it yet. By late November we noticed the plug had melted the outlet's plastic plate cover on one side and scorched the other, though outlet is still usable. I stopped using my car's charger and haven't used since 11/2017 for fear of starting a fire.
I took it in to Ford to see if they could replace it as I see there are several people who had similar problems. Our 1920's house was completely rewired in 2006. We are connected to a public utility and I have had an electrician come evaluate if there was any problem with our wiring. He found NO PROBLEM with our wiring- in fact the outlet still works on the only scorched side. Since it is the wall plate that melted he believes the problem is that the charging unit does not dissipate heat sufficiently. Since the electrician came and checked our circuits and the wiring gauge, and found everything to code, I believe Ford should replace my charger as defective. I can supply photos, if necessary, and the electricians written description of everything. I never used an extension cord because the charger cord was long enough to reach the charging port and our house outlet.
Sounds like you have been thorough in checking it out and taking the extra step of having an electrician examine the outlet was a good idea. The only additional testing that I might do is take a short 12 gauge extension cord and see if the hot plug is on the charge cord end or the outlet end. If the charge cord plug gets hot again then I think you have proved the charge cord is the problem. If the heat is at the outlet then there is still a problem at the outlet end.
Another test would be to charge using a different outlet location to see if the heat problem is still present. Of course once the cord has overheated it might be compromised at this point and be a problem anywhere it is plugged in.
I have found that cheap outlets (The under $2 variety) Often can't support the long duration high amperage (12 or more amps for most of the charge cycle) as well as a high quality outlet can. If the outlet uses pushpins for the wires rather the the screw terminals, that is also a problem, since the wiring contact area is less and makes the outlet more likely to get hot under the high load.
When you take the cord in for replacement make sure to emphasize that the charge cord is a safety hazard. This wording is more likely to get their attention and help justify replacing the charge cord.
Hope they do replace your charge cord.