I did similar experiments and didn’t come with a satisfactory answer. That is why I answered the way I did. Hope @ajax got what he wanted. 
@Claes I use Celsius.
Yes, and also the camera’s particular spectral response, I’d surmise.
Post-processing tools like Color Temperature and Exposure are actually “compensations”, attempting to deal post-priori with phenomenon relevant to the moment of image capture. And I think, as @Morgan_Hardwood’s experiment suggests to me, using a post-processing Color Temperature tool that doesn’t start with good information on the original light and sensor characteristics is really just an arbitrary color manipulation tool.
Edit: Okay, maybe a little heavy-handed coming from a neophyte like me, but I am interested in what more knowledgeable folk think about it. It’s all about learning…
Yes, IIRC the temperature and tint depend on the camera input profile.
Well now, when I posted my question I was thinking the answer might be simple. Little did I know that such an extensive lesson in photo editing would unfold. While I’m most grateful for the lesson and still have a good bit of reading left to do in order to complete it one take-away of mine is that Morgan got to the simple answer when he said, “I’m not aware of a way to calculate it if you’re working with a non-raw file.”. When composing my question I was hoping that “determined” might be even simpler than “calculated” but calculate would do. Unfortunately it looks like it is lost. Although, another take-away is that this doesn’t seem to bother you more experienced photographers and I need to be trying to join you.
Morgan’s test was very thorough and certainly beats anything I’d done in the way of an actual experiment. However, his mind seemed to be exactly where mine was when thinking there could (maybe should) be a more positive answer that fit with the new GIMP CT Tool. In that, there is a known value for CT when the raw file is developed and, like I suspected, this is what GIMP was meaning by “Original Temperature”. I was also thinking that maybe it would be worthwhile for me to keep track of that value (degrees kelvin) for the raw files that I develop. However, I think Morgan’s test also demonstrates that a CT value is not sufficiently precise to be transferable from one editing program to another. While it still seems like preserving this “As Developed” CT value could be of some use, at least as much as a lot of other metadata that is being kept, there are limits to how useful it might be.
Many thanks to all for your willingness to engage. I hope my question did not create too big a distraction from other things you might rather have done. I now have some more topics on my study list which need attention.
Your question was timely in my case; I’m writing a white balance tool for my software and was wrestling with what was pertinent and what was not.
What I’m gearing up to do is to write a “mechanic’s tutorial” on raw processing, starting with the really raw data array and stepping through the operations needed to get a basic usable image. The similar G’MIC tutorial that uses dcraw and the gmic command line tool were invaluable to me in learning this, my thought is to step through screen shots of my hack software that will provide both a sequential depiction of tools and the respective histograms. Some of what will be illustrated is very material to the question we’ve just discussed here, and may provide perspective for your other questions.
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!
That is exactly what I’ve been gearing up to do over the last few weeks - a workflow from the moment the photon hits the sensor till you have a ready image. I read something along those lines some years ago, IIRC it was about demosaicing etc a raw file using ImageJ - have you seen that article? I specifically want to focus on the color aspect of it, as that part is still a mystery to me, I only know parts, and it would be nice to lay out what happens to color during the whole process.
Would you be interested in collaborating on this, perhaps writing it in this wiki-forum?
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Sounds like something I’d be very interested in reading/studying. How are we students to find it when it’s ready?
I’d love for this to be an article on the main pixls.us!
I made a critical mistake last night, ubuntu prompted “upgrade to 18.04?” and I said yes…
Once I get that all sorted out, I’ll proceed…
Did Ubuntu social engineer the consent? 
I click on YES out of habit to my detriment.
I have it all sorted out, but not before I inadvertently wiped my home directory 
Lesson learned: don’t multitask during OS upgrades. That, and Wayland way-laid me…
Not a great loss, most of my important files are on my Windows tablet. Will have to re-calibrate my display, lost that profile, but actually starting to build rawproc from scratch turned out to be beneficial in that I found almost all of the prerequisite libraries in their current versions in the distro. I only had to compile wxWidgets 3.1.1.
Oh, back to color temperature… sorry.
@ggbutcher , @Morgan_Hardwood - probably these are far too basic and simplified for what you are planning to write. But if you haven’t seen these two articles, maybe they might be helpful:
https://ninedegreesbelow.com/photography/dcraw-float-c-code.html
https://ninedegreesbelow.com/photography/dcraw-c-code-annotated.html
(actually this page just provides a link at the bottom to the actual article, which I’m trying to hide from google’s search engine).
I’ve spent hours poring over the dcraw-float-c-code article. It’s where I developed my first understanding of color management. Now, if I could only tease the semantics out of wavelet_denoise…
I did a “stream of consciousness” dump of what I have in mind here:
http://glenn.pulpitrock.net/Individual_Pictures/raw_processing/
Needs considerable work, first off to replace the blackwhitepoint part at the end with a curve that would graphically illustrate the task. My OCD sidetracked me into the Raspberry Pi thing, but I’m going to commence working it as fall cools the air…