What makes a blue color "warm" or "cool," and how do cerulean and ultramarine fit into the mix?
There is much debate over the color temperature of blues. While blue is generally thought of as a relatively “cool” color on the palette, one shade up from violet, within the range of blues, a blue can either be comparatively cool or warm. Which relative temperature a particular blue is, however, is open to interpretation. Some artists say that ultramarine blue is cooler, while cerulean and phthalocyanine blue are warmer; but others say the reverse.
The temperature of a color is always a relative measure; a color can't be cool or warm by itself, it can only be "cooler than" or "warmer than" another color. What establishes that relative coolness or warmth is a matter of opinion.
There's no argument about the location on the color wheel for the different blues. For example, on the traditional color wheel, ultramarine blue is closer to violet, while phthalocyanine and cerulean blues are closer to green. Violet is closer to red, and green is its complement on the color wheel, so you could decide that ultramarine is warmer.
On the other hand, if blue's bias is towards green, then it must also contain a bit of yellow, since blue and yellow combine to make green. And yellow is indisputably a warm color (at least compared to other colors). Also, since ultramarine blue's bias is purple, that would make it a cooler color since purple is the complement of yellow.
However, the issue is by no means settled. Many established artists have decided opinions of their own.
In her article "Warm or Cool? Ultramarine Blue vs Thalo Blue," colored pencil artist Sharon Hicks reports that years ago she was taught that ultramarine blue was cool and phthalocyanine (thalo) blue was warm, but she has also more recently come across articles saying the opposite. She believes that is because instead of using the traditional color wheel, more people today use the color spectrum, which is the conversion of the visible light spectrum into a new color wheel. On the cool end of the color spectrum, violet is cooler than green, and so the violetish ultramarine would be considered cooler than greenish thalo or cerulean blues.
Creating a secondary color such as purple by mixing red and blue is very tricky because you can't just use any blue or red. In fact, if you're not careful, you might unintentionally be mixing all primaries of the color wheel—red, blue, and yellow. Where does the yellow come from? Yellow comes in the warmer blue, and in the warmer red. Therefore, it makes sense that the purest purple would come from the cooler red and the cooler blue.
When mixing blues and reds to make purple, ultramarine blue and alizarin crimson give the purest purple. When you use ultramarine blue and cerulean blue that ultramarine blue tends to recede and cerulean blue tends to come forward, as is the general rule for cool and warm colors.
For resolving this matter, it is best to try your own hand at mixing colors, using different combinations of blues and reds to create the purest purple you can. For example, try mixing cerulean blue and ultramarine blue with cadmium red or alizarin crimson in different combinations. However you decide to classify your blues, the important thing is being able to control what they do on the canvas, how they mix with other colors, and how they relate to adjacent colors.
Note: Cobalt blue is generally considered to be primary blue and the most "pure blue."