First off, color temperature is but one axis of what we call white balance or color balance. Color temperature is based on the light emitted by black body radiators at different temperatures expressed using the Kelvin scale. It runs from amber/orange on one end to blue/purple on the other. Roughly orthogonal to the amber ←→ blue axis is the green ←→ magenta axis. Two light sources with the same basic color temperature can have radically different "tint", which is how we often refer to the green ←→ magenta axis.
With the sun, the only place it is always exactly the same in terms of white balance is in outer space. From anywhere on the surface of the earth atmospheric conditions and the angle of the sun in the sky will affect the exact color temperature and even the tint of daylight.
Even with a cloudless sky there are still factors such as particulates in the air that can alter how the atmosphere filters sunlight passing through it. Recent volcanic eruptions, even halfway around the world, can have anywhere from a subtle to a dramatic effect. So can local conditions due to man made or natural sources of dust or other small airborne particles. This also includes the amount of water vapor which has not condensed on particulates matter to form clouds. Likewise, one's position relative to the equator and poles will affect the amount of ozone in the upper atmosphere over one's observing position and ozone concentrations also change for a specific location over time.
Then there are color casts on any potential subjects due to the reflectively of other things around them. Light from the same sky will look very different on the same person standing on white or beige beach sand than it will if that person takes a few steps to a place where they are standing on lush green grass.