This is Janny Wurts' Cycle of Fire series, consisting of Stormwarden, Keeper of the Keys, and Shadowfane. The first was published in 1984, and the others in 1988.
The main character gains power over wind and waves. His rival has power over flames, and is much stronger, but the process of gaining that power makes the fire mage become violently insane. Because of this, the Firelord (I believe that's what he is traditionally called) is disklikeddisliked and mistrusted by the rest of humanity, though he plays a part in defending them against 'demons'. I don't remember much about the small animals burning, but I think that was part of the process of gaining his powers. He is linked telepathically to them via colonies of alien crystals, which are the source of all the three major mages' powers. (There are other wizards/psychics mentioned in the stories, but I don't think it's explained what the source of their powers is).
The third major 'mage' is a girl who has the power to enter dreams.She She gains that power while hibernating in a spaceship.