How did temperature affect the peak wavelength of blackbody radiation in Planck’s work?

In the context of blackbody radiation, the relationship between temperature and the peak wavelength of emitted radiation is characterized by a shift toward shorter wavelengths as the absolute temperature of the body increases.3

While Max Planck formulated his radiation law to resolve the "ultraviolet catastrophe" by introducing the concept of quantized energy, the specific observation that the wavelength of thermal radiation most copiously emitted by a blackbody is inversely proportional to its absolute temperature is known as Wien's displacement law.12

As a body is heated to higher temperatures, the total energy radiated increases, and the intensity peak of the spectrum shifts from the infrared toward the visible range of the electromagnetic spectrum. Planck’s mathematical model successfully accounted for this distribution by incorporating temperature ($T$) and Planck’s constant ($h$) to describe the energy radiated per unit volume.32