"If it is known, ... , why wouldn't it be provided?"
Interesting topic. Lets analyze a bit here. I will assume you always shoot Raw? Do you know what Raw actually is? I will assume not. Raw is the data the sensor captured, all of it. It is just luminously, or B&W. There is no color, therefore there is no WB or color temperature. Raw can not be viewed like a jpg can. A Raw file is not an image like a jpg is.
"Such is the purpose of metadata."
It is the purpose of the metadata tag to tell whatever viewer you use how to display the Raw data file. It converts it to a jpg. The WB or color temperature you selected in camera is what the viewer (metadata tag) uses. This in no way has an effect on the Raw data file. If on the other hand you shot your photo in jpg to begin with a WB or color temp it is set and baked into the image.
Am I getting any closer to what you want to know? 
@ebiggs1 wrote:...
Am I getting any closer to what you want to know?
Yes, I think your are beginning to understand where I'm coming from.
I somewhat recently (a bit more than a year ago now) went and bought a new Canon camera so that I can obtain raw files. The premise being that raw files preserved quality (primarily the bit depth of color) and offered more opportunity to affect the final result through user control of the image editing. I've only shot raw with that camera.
Contrary to the impression I seem to have made in this discussion, I think, I have a pretty good grasp of what the raw data is and how it differs from standard format digital image type of files such as JPG. While I don't use JPG at all during editing the reason I think it's been used so much herein has to do with the fact that it is pretty much the universal format for files developed by digital cameras which does have something to do with my question because they deal with WB without user intervention in the development process.
I believe that the "LR" in the image you included might stand for "Lightroom" which I recognize as a commercially available software product used for image editing. As it happens I've never experienced LR. I'm a fan of open source software which is by now much more embedded in my DNA than anything to do with photography. The software I've been experimenting with includes Canon DPP (i.e., came with the camera), which has something to do with why I posted this question here, GIMP, and Rawtherapee (RT) which all work on Windows. Possibly you're one of those guys who bought a Mac in order to run LR.
From that one screen-shot I can't tell everything there is to know about LR but a basic question is "does the WB tool show you the temperature without your having to do anything?". If so that is also the way RT works. RT opens initially with what it calls the "Camera" provided WB. On the other hand DPP does NOT show a color temperature until you select that as the method of adjusting WB. The value that DPP shows seems to always be 5200 no matter what raw file has been opened. Interestingly there is a metadata element called Color Temperature in the raw file with a value of 5200. On the other hand RT initially opens with a different value for each raw file and that value is NOT contained anywhere in the metadata. I've also observed that when I select the "Color Temperature" option using DPP that the preview image changes suggesting that the initial preview image used something different than 5200. My supposition is that the 5200 value that DPP forces the user to start with might be related to the camera setup and may or my not be supplied by metadata. On the other hand RT must be performing some kind of algorithmic analysis of the raw data to come up with the value it initially sets. My guess is that LR may be more like RT in this respect.
If we stick with this scenario the user can then adjust the temperature to their liking and then export the results of the editing session to a standard format image file. I'd be using uncompressed TIFF (16bit to preserve color depth) but it could also be JPG (which would have to be 8bit color depth). At this point I would know the color temperature that applied to the subject image file. My question was simply can I come back later and determine what it is by examining the file.
I suppose for those, possibly including you, who do all of their editing with the same raw processor it is possible to retain a copy of all of the necessary file/s such that you can return to the raw processor and make further adjustments to WB. Because raw files are at least partially non-destructive (i.e., raw data is never changed) this is likely to take at least 2 files.
All 3 of the programs I mentioned using myself are capable of editing the standard format image that is produced from the raw data. While DPP prohibits further adjustment of WB, the other 2 do allow the WB tool to be applied to the standard format image files. It seems to me that this is where it would make sense to know the WB and use that as a starting point if such an adjustment were to be made. At the same time, I do recognize that if there was a standard way to do this the subject software could do it as well as I could. The fact that this doesn't happen suggests that if it can be done there is NOT a standard method. Likewise, if it is impossible to do that would explain how the current software works.
It is also my observation that the WB adjustment tools that work with color temperature involve either raising or lowering the value and it is possible that knowing the value used to develop the image in question is meaningless. Likewise, absent a standard method of passing the value from one editing session to another it would quickly be lost when WB is recursively altered in standard format image files.
I do use GIMP which cannot open raw files, a lot, to do post processing on images that cannot be done with other software that is pretty much confined to the development of photographs. For example, I add borders and text to pictures that I intend to print. As such, the raw processor, in my case is seldom where the final editing occurs. As it turns out the GIMP Color Temperature tool requests that the user input the initial value. This suggests that the GIMP developers do not know of a standard method to acquire the value but at the same time leaves one thinking that there must be a reason for allowing the user to input it. RT always starts at 6490 when editing an already developed image (i.e., not raw) file.
If you've read to here possibly you are getting closer to understanding where I'm coming from. My apologies for the verbosity.
"My apologies for the verbosity."
No this is cool, I like this kind of discussion. I do have some points but I don't think I have a real definitive answer except what I actually see.
First, remember you can not view a Raw file. It has no WB. This means your editor or viewer has to give it something. Canon does not document how they make a Raw file. All the other software folks have to make a best guess. And, they all do it differently. So they assign it whatever the tag file recorded from your settings. Only DPP can directly convert a Raw file the way Canon sees it. This is not to say that the others are not doing a good job or even a better job because they do. I prefer Lightroom and Photoshop. Yes, I am on a Windows machine.
When you open a Raw file in Photoshop's ACR (Adobe Camera Raw) converter and make any changes it creates a tag file with those changes. It is an .xmp tag file. It is not part of the Raw file and if it is deleted the Raw file will revert back to its original unaltered state. Further if you do any edits in PS you will now have three files in your folder. A 1234.cr2, a 1234.psd and the tag 1234.xmp.
If I make some edits and save it, then later I delete that xmp file, this photo will come up exactly like this exactly as it did on the first time. Adobe's conversion process does the least amount of processing of any of the popular editors.
I don't want to run down your chosen software down but there is a reason the entire industry uses LR and or PS. Lord knows I have tried a whole bunch of them over the years out of curiosity mostly. None stack up to PS. I will say if LR/PS can't do what you want, I doubt any other editor can either.
One last thing, the reason LR/PS doesn't save the tag (xmp file) inside your Raw file is no other program could read it anyway. DPP does save the tag inside the Raw file but no other program can read it either.
