This should stop the problem.
Direct vent fireplace cold air.
They feature a firebox sealed with tempered or ceramic glass and use a dual purpose vent that both vents exhaust to and pulls combustion air from the outdoors.
If you have not had the original installer over to look at the problem i would try that first.
Traditional fireplaces with dampers wide open pull the warm air out of your house when in use.
Where the controls are located there are usually gas line knockouts holes on the left and right side.
They can be vented both horizontally and vertically.
If it vents through the wall you definitely have a direct vent fireplace.
Proper research prior to installation is the key to simplifying the process.
If the damper is not closed after use they can also let cold air into the house.
That absolute cheapist worst designed direct vent fireplaces should not have cold air coming out of them.
The chimney cap buying guide and the chimney pipe buying guide will help you find out what your options are and how.
A direct vent fireplace does a great job pulling 100 of its combustion air from the outside and dumping the exhaust back outside as well.
The sealed combustion chamber is always seperate from the box you frame in.
Plug the holes with rokwool insulation or high temp caulk.
We have several resources to help.
If you have cold air coming out of the bottem vent there is no way that is coming from the combustion chamber and the combustion chamber is hooked up to the flue.
The bad news is if the fireplace installer does not take care to insulate the fireplace install correctly it will let in a great deal of cold air when dormant.
Fireplace air vent installation can sometimes be difficult to figure out which air intake vent kit is right for you.