Fireplace weatherstripping?

I have a fireplace with a set of brass and glass fireplace doors on it. Because the hearth is not quite level, there are some gaps at the bottom of the door unit, and it allows cold air to leak in to my house and generally make the floor of my living room (where the kids mostly play) freezing. In the past, I h ave used various types of foam weatherstripping in this spot, but the heat from the fireplace will typically deform and melt the foam over time.

Is there a fireproof or heat-resistant type of weatherstripping I can use for this?

How about the woven material they use on ovens and doors of woodburning stoves?

Is the fixture permanently mounted? If so, you might use furnace cement.

Real HVAC tape (what pro’s use as “duct tape”) is actually soft aluminum - real, live metal. I found mine on ebay. If you can move the door out far enough to get 2 hands and a roll of tape down, just run one edge on the door, the other on the hearth. Clean first - you used to be able to get TSP - great cleaner, not so good for rivers. A real paint store should have whatever is being used in its place.
Fireproof, removable, and (relatively) cheap