Axle Retainer Nut Torque w/ Green Bearings?

It sounds like the noise and the heat are unrelated. Seems like a typical amount of heat from what you describe. If it is more of a gear howl instead of a bearing growl, then I would suspect the pinion gear depth is not quite set correctly. If it is not too terribly bad, I wouldn't worry with it. You can always remove the center section and inspect the gear pattern if it is a big concern. The pinion gear contact patch on the drive side of the ring gear teeth should be in the center of the ring gear teeth. Ring gear backlash should be about .008".