Not in general. Colour temperature is the temperature of an ideal black-body radiator whose light appears the same colour. It does not automatically equal the real temperature of whatever you are looking at.

For true thermal emitters that behave roughly like black bodies—such as incandescent filaments—the actual temperature can be approximated by the colour temperature. This is why the term exists.

But many real-world subjects and light sources are not black bodies. LEDs, fluorescent lamps, reflected light from white surfaces, and many materials can have a given colour appearance without being at that physical temperature at all. In those cases there is no simple conversion formula.

If you are talking about ideal thermal radiation, the underlying relationship is described by Planck’s law, and real materials also depend on emissivity and the transmission/reflection of the surrounding medium. That makes practical temperature-from-colour calculations much more complex than a simple formula.

So: colour temperature is useful for describing the colour of light in photography, but it is usually not a reliable way to determine an object’s actual temperature.