George -the reason that they are different is that they use different algorithms to calculate the appropriate colour temperature. I did a more controlled test than you did using three well regarded raw converters.
Here is the test shot:
I used a Paul C Buff Einstein 640 studio flash, with a strip box diffuser. This flash is rated to fire at 5600K ±50K
I manually metered the light with a Sekonic L-358 flash meter. The important number that you can read on the meter is where shows 100%; this means that 100% of the light being metered (and recorded) comes from the flash and there is NO ambient light influence in the image.
Camera settings: Colour temperature set to "flash", ISO 100, 1/125th sec at f/11. The ColorChecker Passport is included in the image as a baseline reference as well as giving me a proper colour correction target. In the test I got a colour temperature reading of the raw file that was opened by the software and then I used the color sampler tool to fine tune the white balance.
1.
DxO Optics Pro 10 - reported colour temperature of
5996K as shot and as
5179K after correction.
2.
Adobe Camera Raw - reported colour temperature of
6150K as shot and as
5000K after correction.
3.
Phase One Caoture One 9 - reported colour temperature of
6817K as shot and as
5371K after correction.
So as I wrote before, the different raw converters use different algorithms to calculate the colour temperature of the image and would therefore be expects to produce slightly different results.
By the way, we say "red hot" and "white hot" in English.