The first point is that 'warm' and 'cool' are relative terms. It depends what you are comparing it with. So while in general blues are cool and yellows and reds are seen as warm, when you compare various blues, some will also be warmer or cooler than others.
Why is it important?
Warmer colours appear to come towards you, cooler colours appear to recede. So if you want to make an object appear further away you cool it down for example you might make it more blue or if it is blue, make it a cooler or a more neutralised blue.
The second point is that temperature is only part of the equation. The colour intensity is another. How much light does it reflect? Yellows reflect the most light, purples the least, but yellow is not the warmest colour, nor purple the coolest. Orange is actually the warmest colour - it is made from two warm colours (yellow and red). A cool blue - such as phthalo blue - is the coolest colour. This can cause confusion since phthalo blue is so intense and bright.
How does it work for painting?
A cool yellow (lemon - leans towards green) mixed with a cool blue (such as phthlao blue - leans towrads green) will mix super bright intense greens as there is no red in the mix to dull it down.
A warm blue (ultramarine - leans towards purple) mixed with a warm yellow (Indian yellow/hansa yellow deep etc - leans toward orange) will produce dull greens as both the yellow and blue have some red in them to dull the mix.
Here are some examples.
There are many pigments used for cool yellows, including Hansa Yellow light PY3, cadmium yellow light and PY35 and lemon yellow PY175.
Warm yellows will easily mix bright oranges, especially when mixed with a warm red as there would be no blue in the mix to dull the mix down.
A yellow that is between these two, a mid yellow, doesn't lean towards green or orange so will work as a primary yellow. My favourite is Hansa Yellow Medium PY97 but there are other excellent mid or primary yellow pigments.
As there is so much yellow in this red, it won't make purples.
This is a cool red. It leans towards purple. It is also a primary red as it will mix clean purples and clean oranges. This is PV19 - Quinacridone Rose.
Mixed with a warm blue such as ultramarine, you can create gorgeous bright purples, however this pigment is so good at mixing purples that you can mix it with almost any blue and create lovely purple and violet hues.
This is a warm blue - Ultramarine. Made with PB29, this blue leans towards purple. It will make duller greens when mixed with a yellow than you'd get with a cool or green-biased blue.
Mixed with the PV19 above, it will create lovely purples.
While I don't generally worry too much about whether secondaries are warm or cool, a general rule is that if a green leans towards yellow it is warm; if it leans towards blue it is cool. If a purple leans towards red it is warm; if it leans towards blue it is cool. If an orange leans towards either red or yellow it is still warm, however if it is neutralised by adding a little blue, it can be cooled down. So burnt orange, burnt sienna and burnt umber - all neutralised oranges - are all warm but less so than a bright orange.
Earth pigments are all more neutralised as they don't have the high chroma of the bright reds, yellows and blues. They may be still considered warm or cool, but they are all 'cooler' than their primary counterparts. so yellow ochre is a neutralised warm yellow; raw umber is a neutralised cool yellow.
Happy painting.
