All but one of mine use the cool side for their "fecatorium" (yes, that's herp talk for bathroom).
As to your plan to acclimate him to you, I think it's at least as important that you are comfortable with the strategy as it is that your pet is. So, yes, try it that way, if he climbs into your hand you should feel free to pick him up. Just remember that he may bolt, so don't lift him so high that he'll get hurt in a fall. Also, if he does start to bolt, be very careful not to grab his tail or it will snap off. I'm not trying to scare you out of interacting with him, just want you to have all the warnings it takes.
It sounds like he's eating just fine, I hope this keeps up for you. If I remember right, you're pretty far south, so hopefully you won't have the winter effect that many of us in the north do.
Good luck!
Todd