The color purple, or equivalently violet, is actually on the end of the visible electromagnetic spectrum, having the highest frequency of any light wave. The reason we see different colors is because of this difference in frequency, where violet light has higher frequency of light waves than blue light. Red is the first color in the visible spectrum, having the lowest frequency of light waves. Ultraviolet waves have a higher frequency than that of violet waves, however, produce light waves that are invisible to the human eye, and therefore not on the color spectrum.

The frequency in each light wave is directly related to how much energy a light wave has. If the wave has a large frequency, then the wave is oscillating very rapidly back and forth, meaning it has a lot of energy. This energy is then felt in the form of temperature, or heat.

Thus the colors of light with the highest frequency will have the hottest temperature. From the visible spectrum, we know violet would glow the hottest, and blue glows less hot.

As this is true for all forms of light, its application is seen in fire, or when an object is heated up. A fire will start to glow red at first, which is the lowest temperature of light waves. If the fire got hotter and hotter, the flames would start glowing in different colors, going from orange, to yellow, to white. This is the same for a metal that is heated up. Known as black body radiation, a body of metal will heat up and give off red light at its lowest temperature, and produce higher frequency light at higher temperatures. Violet light can sometimes glow at around 71,000 degrees Farenheit. For reference our sun burns at 8,500 degrees Fahrenheit, glowing in white and yellow!

It's not - purple light is actually more energetic than blue light.

Are you thinking of how weather maps often draw extremely cold temperatures as purple? It's just convention (the answer has to do with how colors on computer screens work). Ice reflects blue light, so cold temperatures are associated with blue. Fire emits red light. However, note that the fire is emitting the light rather than just reflecting it: a flame that is hot enough will emit blue light, and is hotter than the red-emitting fire.