Color temp/ gray scale basically the same thing. Color temp is basically a number/ point given to a various level of the gray scale. You display patterns with various degrees of light intensity from 0 IRE (Black) to 100 IRE (white) and everything in between is some intensity of gray. Typically a calibrator picks a pattern between 20-30 IRE and adjusts the offsets and then picks a pattern between 75-100 IRE pattern and adjusts the gains. The gains and offests do interact and you need to repeat adjusting the gains/ offsets until you get close to D6500 (often referred to as 6500k for simplification to consumers but it isn't technically accurate, D65 is acceptable). Then once a calibrator gets close to D6500 he will verify the whole grayscale and see how the changes are affecting all the IRE levels. This sounds simple but often can take quite a bit of time.
This system might not make sense to a lot of people unless you understand our TV system. Our system as everyone knows was black and white initially. When they decided to introduce color in 1953 they didn't want to make the black and white TVs obsolete. It would make a lot of people angry that spend BIG bucks on a TV. So they decided to send two dofferent signals. The black and white picture carries the pictures detail and on a second radio carrier the color information is sent and the color information was added to the black and white picture. Think of it as painting by numbers.
When using color TVs that make their picture using red, green, and blue you can understand the importance of getting the grayscale signal correct. Errors in color are often fixed in the color decoder section of a service menu where the color signal is processed. At the user level the color information is adjusted with color, hue, tint, saturation, etc. parameters.
BTW, High def still didn't make black and white obsolete. If you connect just the green wire to a composite feed on a black and white TV you will still have a black and white picture. Although, on color TVs it will be green without the red and green wires.
For the other calibrators here. I know I simplified some of this for less technical people can understand it. If you'd like to get more detailed be my guest I just don't wish to be typing all night