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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 at all temperatures (with the scale varying), with the peak wavelength λpeak occuring at:

λpeak = b/T,

where b is Wien's displacement constant and T is the absolute temperature.

In S.I. units, b = 2.898×10−3 m·K to four significant figures (the unit is metre-Kelvin, not millikelvin).

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Q: How do wavelengths of radiant energy vary with the temperature of the radiating source?
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