What Type of relationship exists between the Temperature of a Star and the Wavelength of a Star?

This is known as Wien's Law:

The relationship is:

wavelength = 0.0029/temperature

It is an inversely proportional relationship.

To estimate the surface temperature of a star, we can use the known relationship between the temperature of a blackbody, and the wavelength of light were its spectrum peaks. That is, as you increase the temperature of a blackbody, the peak of its spectrum moves to shorter (bluer) wavelengths of light.