Do different colours all have different temperatures? what are they? I know that the infrared spectrum is heat, so that must mean the whole spectrum is the same, right? What is the difference between light and temperature?
As you heat an object it glows with a different color.
First infrared, then red (ie red-hot) then white then blue
Color temperature is a measure of how hot a glowing object (like the sun or a light bulb) would be to give the same color.
The sun is around 6600 deg, so to get the same blue-white light from an artificial source you need to heat the lamp to the same temperature (or mix red and blue light in the correct proportions). Regular light bulbs are much cooler, around 2500 deg so look much redder on photographs.
The temperature is measured in kelvin (K) which are like deg C - except they are no negative values. 0C is 273K and 100C is 373K so at the temperatures of lights you can think of it as deg C.
Basically there are three elements here to know about:
1) an arbitrary spectrum where each frequency gets some intensity
2) a temperature and its corresponding black body spectrum (see top picture in the above link). this represents a specific spectrum that photons have if they happen to equilibrate with the object at that temperature
3) colour vision of the human eye knows about three values (roughly R,G,B)
Now what are the connections?
Now for each (1) you can calculate (3), but many spectra will correspond to the same colour (triple).
For each (2) where you have only the temperature parameter to adjust, you can also calculate (3), i.e. a colour triple, but this way you won't get all available colours.