Leo is attempting to narrate the events of a particularly important period in his life. After the "Hot Seat" fiasco he worried that the open hostility towards Stargirl shown by the other students—as seen in impertinent questions such as "Why can't you just be normal?"—would spill over into the classrooms.
Leo never thought that the Hot Seat business was a great idea in the first place. He felt a profound sense of dread on seeing that Hilari—who positively hates Stargirl's guts—would be serving on the jury convened to ask her questions. And after the whole farcical experience ended, he worried that the nastiness displayed during the Hot Seat episode would contaminate the whole school, making life so much harder for Stargirl.
So where does all this leave us with the original question? Well, Leo wants to give a truthful, objective account of what happened in the wake of the Hot Seat disaster. But at the same time he's also developed an emotional attachment towards Stargirl, which he's keenly aware will make him a less reliable narrator.
This is what he means when he says that the heart and head are contrary historians. The head, the rational faculty, gives us one account of events, whereas the heart, the emotions, gives us another one entirely. And the two have melded together in Leo's mind, meaning that the events in the aftermath of the Hot Seat farrago have become somewhat blurred in his mind. Leo really wants to give an accurate account of what happened, but his emotions have got in the way, making it almost impossible for him to do so.