Anytime you move towards blue on the color wheel, you get a cooler color. Anytime you move away from blue, you get a warmer color.
Let’s look at green, for instance. Green is between yellow and blue on the color wheel.
Cool green is blue-green
If you move towards blue, you get blue-green, which is cool.
Warm green is yellow-green
If you move towards yellow, you get yellow-green, which is warm.
What about blue itself: Is there such a thing as warm blue?
Yes. When blue moves away from true blue and towards yellow, you get green-blue, which is warm blue.
Wait a minute. Doesn’t that mean “warm blue” is the same thing as “cool green”?
Yes! Some colors are definitely “blue,” and others are definitely “green,” but the exact boundary is subjective and depends on context.
What about when blue moves towards purple/red?
In that case, the resulting color is not “warm blue;” it’s “cool purple.”
Anyway, here’s a handy reference chart.
(Sorry it’s so ugly. I made it for myself when I took a pastel drawing class a few years ago. I’ll make a better one for you eventually.)