Mars, a fire planet, was so fiery that it was placed in Scorpio " to temper it" (Pliny?)
I believe Jupiter/Air, since air is moist, was placed in Sagittarius for the same reason. When reading tarot and doing dignities, I count WoF as Air, not Fire.
No, that isn't the rationale. Mars is intemperate, as is Saturn, Mars too hot, Saturn too cold. Mars was given to the nocturnal sect to temper it a bit, just as Saturn was given to the diurnal sect to temper it a bit, in Saturn's case to warm it up some.
The intemperate planets are considered malefic in traditional astrology. They're considered too hot, in the case of Mars, and too cold in the case of Saturn to help sustain life.
Jupiter is moderately warm and wet, which makes it a benefic. Venus is moderately cool and wet, also a benefic.
Jupiter in Sag trines the Sun in Leo in the thema mundi, so we know that Jupiter and trines have some things in common. It also trines the moon in Cancer from its night house, Pisces. They're alike. Saturn is like an opposition, because it opposes the sun and moon from its signs of rulership. Saturn rules Capricorn and Aquarius, which are opposite to the signs of the moon, Cancer, and the sun, Leo.
Mars is like a square, because it squares the sun in Leo from Mars' house, Scorpio, and squares the moon from its day house, Aries.. Venus is like a sextile, because it sextiles the sun from its house, Libra, and sextiles the moon from its night house, Taurus.
Mercury is too close to be like a proper aspect, and it rules the signs to either side of the sun and the moon, Virgo and Gemini. Mercury is the most changeable of the planets.
Again, this comes from a pedagogical device used in Hellenistic astrology, the thema mundi, or chart of the world. Someone passed on a nice article about it to me, if you want to learn more:
http://www.azastrologers.org/Articles/NoblehorseThemaMundi.pdf