Back to the original question, “How is the value for Original Temperature calculated?”
I’m not aware of a way to calculate it if you’re working with a non-raw file.
A test.
Here is a raw photo in RawTherapee, the white balance temperature is too high at 7600K, making the whole image too orange:
I saved the too-warm image as a 16-bit PNG file for later use:
I use the white balance picker to make the paper in the background neutral, which sets the temperature to 4500K:
Now open the too-warm PNG file in GIMP. Ideally GIMP would also have a pipette allowing you to pick a spot on the image which should be neutral, to calculate the optimal temp and tint for you, but GIMP 2.10.4 doesn’t have that yet, so you have to adjust the temperature manually.
GIMP does not know the original color temperature (how could it), so it sets both original and intended temperatures to a reasonable 6500K:
We know from RawTherapee that the correct temperature to balance the whites is 4500K. If you adjust the intended temperature in GIMP to 4500K, you get this:
The image still has an orange/yellow tint, because the source temperature is incorrect.
If you adjust the intended temperature visually to taste, you may arrive at 4000K which gives you this:
That is the best I could do, acting like I don’t know the source temperature. Note that the paper is close to neutral, but the rest of the photo still has a tint (the red flower is a dirty orange-red), and it does not match the correct 4500K image from RawTherapee.
If I set the intended temperature any less than 4000K it would make things even worse - the red flower is now less orange, closer to red but still “dirty”, and the paper has now turned bluish:
We cannot properly correct the white balance through setting the intended temperature without knowing the original temperature.
I was under the impression that if I set the original temperature to 7600K, which we know to be correct as that is what I set when I saved the image in RawTherapee, then setting the intended temperature to 4500K would result in an image identical to the 4500K one from RawTherapee, but it did not (compare this to the second RawTherapee screenshot):