How does heat sensitive paint work?

Heat sensitive or Thermochromatic paint is made with Liquid Crystals or Leuco Dyes. Liquid crystals are used in precision applications, when accurate temperatures ranges are required, however the color options are limited. Leuco dyes allow wider range of colors but response temperatures are not accurate.

Liquid Crystals

The orientation of the molecules changes with heat, this gives them periodic spacing. The light passing through the crystal is detracted, and the wavelength with the greatest constructive interference is reflected back, this is perceived as a spectral color. 

Leuco dyes

They are usually in the form of microcapsules with the mixture sealed inside. They are usually used in combination with some other pigment, producing a color change between the color of the base pigment and the color of the pigment combined with the color of the non-leuco form of the leuco dye. The color change usually happens in 3 °C (5.4 °F) interval.