How are temperature and color linked?

Answer 1

Colour and temperature are linked internally

The more you provide temperature the more the atom of that material gain energy and hence they emmit excessive energy in either visible spectrum of light or invisible spectrum in electromagnetic spectrum

Example

If we heat iron it glows bright red that is it radiates excessive energy in the form of red colour( as we percive)

Answer 2

Temperature and color are linked through black-body radiation, where an object's color changes as its temperature changes. As objects heat up, they emit light at different wavelengths, causing changes in the perceived color. For example, a blacksmith's iron will first appear red, then orange, and finally white-hot as it gets hotter.