When you consider the total heat given off by an open fire place versus the amount of household air that goes up the chimney throughout the burn cycle, an open fireplace may warm up the room it is in, but it delivers a net energy loss to the house. It is in fact a wintertime air conditioner because of all the cold air drafts it sucks into the house.
Putting good glass doors on an open fireplace will reduce the heat that gets to the room somewhat, but will cut down a lot on the air that goes up the chimney. Essentially, glass doors will take an open fireplace from a net energy loser to a small energy gain. This wood burning device is still nowhere near as efficient as a fireplace insert or a wood stove, but it is certainly less of an energy guzzler. Probably the greatest benefit of have closed glass doors is that there will be less of a tendency for backdraft towards the end of the burn.
Ceramic glass will let more heat into the room and be safer than regular tempered glass. The nice doors that we showed on TV came from The Fireplace Shop in Toronto.