A hot object shines brightest at a wavelength, in micrometres, of about 2,900 divided by its temperature in kelvin.
Wien’s displacement law: the peak of a black body’s curve sits at 2,898 micrometre-kelvins divided by the temperature. The Sun, at 5,772 K, peaks at 0.50 micrometres, in the green; a person, at 310 K, peaks at 9.3 micrometres, in the infrared, which is why a thermal camera works at 8 to 14. Double the temperature and the peak moves to half the wavelength.
It is the peak per unit of wavelength; per unit of frequency the peak is somewhere else. It is the brightest wavelength, not the colour you see: the eye weighs the whole curve, so the Sun peaks in green and looks white. It holds only for a thermal radiator close to a black body, not for LEDs, fluorescent tubes, the sky or a laser, and real surfaces radiate less (and unevenly) because their emissivity is below 1.
Estimate with the rule, then check it against the calculator that models it properly.
Open Black Body & Colour Temperature →