If you read the specifications for unvented gas logs, you'll find that they usually specify that the equipment not be used for heating, and often have limitations on how many minutes in an hour of continuous operation are recommended.

Unvented equiopment is, oh, 200 times or so as likely to injure people as vented equipment. It probably CAN be safe if all the recommendations for maintenance and safe operation are followed by everyone using the equipment, but I don't think I ever found anyone who ever read the lengthy list of warnings, much less followed them.

My recommendation is to install vented fireplace logs, or to spend the extra money to get a gas fireplace insert, which is what you should do if you want a reasonably safe and efficient source of gas heat from your wood fireplace.