Green is generally seen as a cool colour, even though it is a mixture of a warm and cool pigments. What is purple? I'm not sure I've ever heard it listed as warm or cool. I'm inclined to say it is cool, but since I obviously have no feel for this subject, you'd probably be better off assuming the opposite if you aren't sure.
Traditionally, of course, purple is the colour of nobility. The only purple dye in antiquity was obtained by extracting mucus from the murex sea snail, which was hard to find and expensive to process. I don't know why they couldn't mix red and blue, but I suppose there must have been reasons.
Purple is associated with girls these days. Some purples are, admittedly, extremely close to pink, but since purple is a mixture of red (i.e., dark pink) and blue, it doesn't seem like it should be particular to either sex. Wikipedia has a discussion of how purple is different than violet, but I have to admit that it totally escapes me. If we distinguish three primary colours, and if we distinguish green and orange as secondary colours created by mixing two primaries, why should distinguish more than one colour as the mixture of red and blue? I won't argue that there aren't good technical reasons, but, whatever they are, they are beyond my comprehension.
Some people are really into purple. I saw a magazine spread once on a woman whose whole house was purple -- purple paint, purple furniture, purple rugs, and she even served purple food (blueberries, chiefly). The names of purple shades -- fuchsia, mauve, lavender, lilac, amethyst, and periwinkle -- sound exotic, but most of them are just flowers. I always hated fuchsia until I learned how to spell it, but why is it pronounced so strangely? I don't know. The colour is named after the flower, which was named after the German botanist Fuchs (sort of rhymes with "books"); perhaps the person who named it also gave it the bizarre pronunciation. There is also a "fashion fuchsia" that is more like hot pink. The most interesting shade of purple, historically, is mauve (rhymes with grove). It was named in 1856 when William Henry Perkin discovered a residue from his attempts to create artificial quinine, and became commercially important as the first aniline dye -- the beginning of the chemical dye industry. The 1890's in America have been described as "The Mauve Decade," not only because the colour mauve was popular, but also as a derisive commentary on the pretensions of the era. The derogatory sense of mauve comes from James Whistler's dictum that "mauve is just pink trying to be purple."