Don't you think your h needs to earn your trust and be transparent with his email and cell phone accounts? He has to do the necessary work on himself and if you are willing to give him the milk, then why purchase the cow?
You need to take things slowly because if you are willing to allow him back in the bedroom this quickly and sweep everything under the rug, then what has he learned? The answer is: he can cake eat and you are more than willing to open the door and let him in no matter what he's doing or done to you and your family. He needs to earn your trust and respect and start out as friends and go from there.
Pretending that this situation has never happened and working through the issues that got your marriage to where it is, have to be worked through, i.e., acknowledged and discussed and worked through by both parties. Sweeping it under the rug will only cause the mess to come out again at a later time.
I can't read his mind...but who knows...he may be thinking of a nice booty call because no one else is available. Also, before having sex w/this man, he would need to have himself checked out for stds. Why? Because you don't know who he has been with and before you say he wouldn't do it...he most likely did.