Gas fireplace & weatherstripping

In checking the house for air leaks, I've discovered there's about a one inch gap between the wood facing that surrounds our original equipment vented gas fireplace and the metal frame surrounding the glass doors, and a substantial amount of cold air is flowing through.
As the fireplace is gas,we already have to leave the flue damper open and I'd really like to seal this leak up.
I've temporarily placed the kind of foam weatherstripping you use around window a/c units to seal the gap, and if there's no safety issue, I'll probably just leave it there. Does anyone have any thoughts on this?
Thanks, and happy new year.
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It it is not a zero clearance insert there is a safety issue. There are fire proof insulators. Check with a fireplace insert store or Home Depot might even have it.

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Well, I'm not sure exactly what a zero-clearance insert would look like, but the wood molding that surrounds the firescreen is flush with the metal frame at the bottom of the fireplace. The gap widens as you go up, i.e. either the firescreen or the wood is not installed 100 percent vertical.
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A zero clearance unit allows combustible in direct contact with the unit. Mine is basically a doubled walled unit with ceramic glass. The inside box has an intact and exhaust duct going up the chimney. The outer chamber is where it sucks in air from the house and heats it and sends it out into the house. It is close to 90 percent efficient like a furnace. They are great. There house air is never mixed with combustion process.

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