@Commodore
Might it be a matter oft musscle relaxation in your back?
I've thought of that and that seems to be my wife's take on it as well. I do sit a lot throughout the day due to my job, which does cause tension in the lower back so this might be the most likely culprit.
Does the skin get sore (just for clarification)?
No, the skin doesn't get sore. It feels like the muscles (or possibly the kidneys themselves, it's hard to tell) that get sore.
I did find someone else online who has this issue too and the explanation they got from their doctor was it has something to do with breathing habits for those who take really hot showers. According to this doctor, when you take really hot showers, you tend to breathe shallower and less frequently without even noticing you're doing it. Apparently this can cause something called respiratory acidosis temporarily as the kidneys attempt to compensate for the increased levels of CO2 in the body.
Of course this is coming from someone online who claims this is what their doctor told them, so I'd have to ask my doctor about it before running with that diagnosis.
Have you ruled out something like fibromyalgia?
I haven't ruled anything out since no one, not even my doctor, has been able to give me a clear answer on this.