Wiring a water heater with 3-wire 240v are warm

GE water heater 40M06AAG - (40 gal)
upper 4500w@240v* 3380w@208v
lower 4500w@240v* 3380w@208v
The wiring looks like #10, bigger than #12 for sure, goes to a dual 20 amp breaker.

In the summers i live in a small house in Montana and replaced the water heater last summer. This summer the installation wiring & caps got hot enough to melt plastic so i know i did something wrong. The wiring is only 3 conductor, 2 black and one white (no ground). Apparently when installing, i duplicated the original wiring by connecting the black wires to the water heater's red and black with caps, which seems reasonable. But the white was grounded on water heater housing which seems weird, as does not having a ground wire. The new WH User's manual was no help at all.

My best guess is that the connector caps were not large enough and the wire wrap they covered was not clean enough, and aging over the fall, winter, spring caused corrosion, which led to enough resistance to generate heat under the caps. So i cleaned the wire with emory cloth and steel wool, wrapped the wires again and capped them with larger caps. But one cap & wire connection is getting quite warm. Not too hot to touch, and not melting plastic but 120-130 degrees warm. Is this OK?


The person who did the original wiring was probably as much an amateur as me. It was his hunting cabin that he improved to get his wife to live here. i am guessing it was wired in the 1970's, maybe earlier. It surprised me there was no ground wire.


Questions:
0. Should water heater wiring ever get warm to the touch?

1. Should this wiring strategy be OK?
If yes, how do improve the connections so they do not heat?
It would seem strange to use solder on house wiring.

2. Should i open the circuit breaker panel to see if the white is running to ground or neutral?
(i cannot imagine how to tell with a VOM. The biggest problem here is that i have never really understood the difference between neutral and ground.)
Which should it be and should i correct it?
Does it really make sense to reconnect the white wire to the WH body?

3. I worry about the water heater not having a proper ground. Should i pound a grounding rod into the dirt directly below the floor and ground it that way?
Or fish a new ground wire thru the walls to the circuit box?

4. Should i hire a professional electrician or buy fire insurance?

Rimini, MT

If you connected one Black wire to the WH black wire and the other Black wire to the red WH wire then you should be correct. The white wire tied to the WH body should be tied to the Neutral/Ground bar in the panel. Until recently the neutral or ground wires were attached to the same bar in the panel. Now they want them separate in some places. You are fine. Some older units were wired with only two wires and no ground/neutral wire at all.
Are you tightening the wire nuts enough to make good contact inside the connection? If your wires are older and you have concerns about them even after cleaning them, I would get some dielectric paste or gel and coat the wire ends before adding the wire nuts. Then when you have tightened the wire nuts as much as possible with your fingers, use a pair of linemen pliers to tighten the wire nut until the wires are twisted a couple of time outside the wire nuts. Be careful not to damage the wire nuts, but with #10 wire it is almost impossible to get them tight enough without pliers. Also check the wires where they attach to the breakers inside the panel. If you have had heating problems then those connections could be loose. Look at your wires on both ends. If they are oxidized or brittle from overheating they may need to be replaced, but probably not.

Make sure all the wires are copper!

#10 on a 20Amp breaker is about all you can do to ward off heating up the circuit.
Yes, I've seen WH circuits run warm but, not enough to melt wire nuts.
White is your ground, connect it to the WH, if your comfortable, open the panel and verify it is grounded.
No ground rod needed.
I suspect the issue is trying to marry stranded wire from the WH to solid core from the breaker panel under a wire nut, you gotta get a good wire surface connection or it will heat up.
You could always tin the stranded wire tip, use a split bolt and tape the crap out of it but, this shouldn't be necessary if installed correctly.

White should NOT be used as a ground, but in your case you really don't have a choice. It's a minor violation to solve a big problem.

The reason the wire nut melted was NOT because it was drawing too much, it was due to a bad connection.