How does the frequency of radiant energy vary with the temperature of the radiant source?

The wavelength of radiation is related to the frequency of radiation. Frequency is the rate of vibration of a wave source. High frequency vibrations produce short waves and low frequency vibrations...

The answer to this is given by Wien's displacement law, at least for an ideal "black body" as the radiating source. The law states that the distribution of wavelengths has essentially the same shape...

"Radiant" just means energy that can move from one place to another without a medium to carry it. So any form of electromagnetic 'radiation' qualifies. That includes heat, light, and radio, generated...

sun

A low temp source emits low-frequency, long wavelength waves. A medium temp source emits medium frequency, medium wavelength waves. A high temp source emits high frequency, short wavelength waves.