I‘ve been thinking more about cool and warm blues.
Let’s take the colour wheel and put that pure blue at the bottom, just for practical reasons. This pure blue is the coolest of the cool, super cool. On the opposite side we habe orange, this should then be the warmest. On the top left and top right we have pure red and pure yellow. They are warm, I would say equally warm, judging from their distance from the orange. No one doubts that if you put even a little bit of blue into that pure red or that pure yellow you cool them down. If you put some yellow into the red or vice versa, you make them warmer. So you can always say if, for example, a red is warm relative to pure red or cool relative to pure red. This is easy.
But for the blue it means that if you put a little red or a little yellow in it you make the blue warmer, because both red and yellow are warm colours. So relative to pure blue all other blues are warm blues. So you can only say if one blue is cooler or warmer than the other. None of them, exept for pure blue, is warm or cool. If, for example, you create a colour with 80% blue and 20% yellow on the one hand and a colour with 90% blue and 10% red on the other hand, the one with the yellow in it is warmer than the one with the red in it, because it contains more of a warm colour and less of the super cool blue. Everything that moves away from the super cool blue in either direction turns warmer. In my example, the blue with the yellow is farther away from cool blue than the blue with the red.
If what I have written above is as far away from nonsense as it can be (or at least far enough), from a physics point of view phtalo blue is actually warmer than ultramarine. Still, most people seem to perceive the opposite. Why? I think it could be because they perceive red as warmer than yellow and so a blue with added red is always perceived as warmer by them than one with added yellow. Also, it’s difficult to see if the proportion of red in one blue is higher than the proportion of yellow in that other blue. So it’s a fight between physics and subjective perception and the point is what of the two we consider more important in art, in painting.