Wood fireplace - How to insulate opening?

[RCGA]

I have a couple of wood fireplaces in my house. Both are older 1960s styles that are original to the home. They're both "open" (no glass), but with a closed damper and unused.

For the past few years, I've shoved a half of a fiberglass bat up against each closed damper. But now with a newborn, I'm trying to move away from the exposed fiberglass.

I would use Roxul, but it's like $100/bag after tax and I only need a bat. I considered some rigid board and foam, but I might sell the house in a year or two and don't want to deal with the cleanup.

Looking for something to stop the hot air being sucked up the chimney.

[A. Spruce]

Install some glass doors on the fireplace, this will stop air flow, improve the looks of the fireplaces, and keep baby from crawling in.

If you don't want to invest in doors, wedge 2x4 flush in the opening and cover it with plywood, remove when it's time to sell the house. If necessary, you can put foam weather strip between plywood and opening.