Why does hot metal glow red and then white?

Because everything emits light according to its temperature, and as temperature rises the emission shifts toward shorter wavelengths and broadens across the spectrum.

Any object above absolute zero radiates energy, with a spread of wavelengths determined by its temperature. This is black-body radiation, and it follows a predictable curve.

At room temperature, almost all of that emission is in the infrared — invisible to us, though thermal cameras see it. As metal is heated past roughly 500°C, the edge of the curve begins to reach into the visible range at its red end, and the metal glows a dull red.

Heat it further and two things happen at once. The peak shifts toward shorter wavelengths — the relationship is described by Wien's displacement law — and the total emission rises very steeply, as the fourth power of temperature.

So the colour progresses through a sequence that blacksmiths have used as a temperature gauge for centuries: dull red, cherry red, orange, yellow, and finally white.

White is the key point. There is no such thing as white light of a single wavelength. The metal appears white when it is emitting strongly across the whole visible range at once, so all colours reach the eye together. It has not started emitting a "white" wavelength; it has simply become hot enough to emit everything.

The same physics sets the colour of stars. Red stars are the cooler ones, around 3,000K; our yellow-white Sun sits near 5,800K; blue-white stars exceed 10,000K. A star's colour is a direct read-out of its surface temperature.

It is also why incandescent bulbs are described in kelvin.