Don't worry about writing too much in your post. The more detail you provide, the better of a response people can give.
Anyway, I think what your boyfriend is going through is what happens to a lot of people when they regain contact with an old lost love. There's a lot of excitement that can come from reconnecting with somebody who's reappeared from the past. It happens a lot even when people find an old friend. However, with an old love it can be dangerous because it can easily lead to the temptation to have an affair. Your boyfriend might not be consciously thinking that he wants an affair. That doesn't mean he wouldn't get swept into it. Unless he's actively got a plan to avoid it, it's likely that he could end up in one before he realizes what he's getting himself into. Just because they had a bad relationship before doesn't mean it won't be easy for him to forget the bad times and only remember the good feelings.
If I was you, I would set some definite boundaries with him right now. If he wants to stay in contact with her, he has to be open with you about all of the communication between them. If he wants to see her in person again, you have to be there too. An affair can't happen as long as nothing is hidden from you. Let him know you have to be welcomed into the friendship as well, or else it won't continue. Just tell him that you would feel really uncomfortable with them staying in contact otherwise. If he cares about you, he'll place you and your feelings ahead of her. Good luck!
“This planet has - or rather had - a problem, which was this: most of the people living on it were unhappy for pretty much of the time. Many solutions were suggested for this problem, but most of these were largely concerned with the movement of small green pieces of paper, which was odd because on the whole it wasn't the small green pieces of paper that were unhappy.” ― Douglas Adams, The Hitchhiker's Guide to the Galaxy