Bearing running hot

I will be watching it for the next leg, and as long as it stays as cool as it is, I wont be doing anything.
If I do mess with it, I will look for that hole. Keeping it under 50C is the goal.

Good for you. I hope you solved it. I'd keep watching it before I backed it off any more. Too loose can be as bad as too tight. Also, check the axle at 90 degrees from where you found the cotter pin hole. Sometimes they drill it there too, and you can get a smaller adjustment than the 1/6th turn.

This morning, I opened the cap.

I backed the nut off 1/6th a turn. You cannot turn 1/4 on a six sided nut.
I also put more grease in the hub.

After a few hundred km, the bearing temperature is now less than 5C than the others.

I could probably back it off another 1/6th turn.

As midnightsadie said, your axle is at risk, as others said....
1. Jack that wheel up and spin, check for over adjusted brake shoe
2. wiggle to check for loose bearing
3. Readjust axle nut to insure not too tight

47 c or 116 degrees doesn't seem bad at all but why the difference compared to the others? I would think that the little difference is attributable to 1. through 3. If not go on to number 4.

4. Disassemble and visual inspection of bearing surfaces. Bearings need to be looked at closely. They will have a swirl or honed like look when new. As they wear they will look smooth with no swirl then they will progress to having a mottled or gravel like look and in last stages they will be deeply pitted and galled looking.
The roller itself will look perfectly smooth. Where people never look when inspecting a bearing is the inner race back behind the caged rollers. They need to be clean and dried and look down in between the rollers at all of the inner surface. I have seen bearings that appear to be ok have bad areas on the inner race. People look at the rollers but dont look beyond them as they would look at the cup side.

If you get to the point of pulling it apart make note of bear and seal numbers so you can carry spares or find the whole hub and carry it.

Under Murphys law that ensures that you will never need it.

Everyone is saying what I am thinking.

I will find out what is going on.

I think the issue is not how hot you can run a bearing. Bottom line there is something wrong with that one. So if you feel lucky, let her rip. Maybe the bake lining is dragging - who knows.

That one is your decision.

jack that one up, give the wiggle test, and a spin test. double check the nut ,to loose to tight, even one hole on the cotter pin makes a difference, I,d do this NOW, a break down on the road could ruin a axle.

Yes, I would be concerned. Could be several things though - you need to disassemble that wheel to see what's going on.
Or maybe it's time to go through all 4 wheels.

Have you jacked and spun it to see if it's running smooth? Could be too loose, or too tight or maybe that one got missed or a brake is dragging?? At least you have 3 other ones to check it against. I think I'd look for a new set of bearings and seal and a tube of grease just in case things get worse.