Madison does not like Adam, not even a little bit. He's a jerk in every sense of the word, and Madison wants nothing to do with him. But Madison can't bring himself to simply leave a mage to suffer when it's in his power to help—and as he is the only available fire mage on campus, he is literally the only one who can help Adam bind his negative energies.
It's the kind of help he'd offer anyone; Adam the jerk is no exception. Once the spell is done, they can go their separate ways, and that will be the end of the matter. Right?