Our house has a large double sided fireplace right in the middle of it. It has a vent above the doors on either side to circulate the hot air, which is not all that effective. I wondered if it would help to have air forced across the firebox and decided to try an experiment. I rigged up a window fan to blow air into the vent in one room.
It actually does help. It makes the living room, on the other side, nice and toasty.
No. The glass doors radiate some heat but not enough to be concerned about.