I believe from your description that this is the premise: You attached a plastic box above the front of a fireplace in a way that is attached from behind to the exhaust vent / flue. You've observed that this installation results in the plastic box becoming heated when the fire is burning, and you'd like suggestions for how to not have the plastic box heat up while the fireplace is burning.

Option 1 -- most effective and less material involved: Remove the plastic box from above the fireplace, and put it somewhere that it is not exposed to a heat source. Depending how you mounted the box above the fireplace, this may involve minor repairs like patching holes.

Option 2 -- more involved, less effective: Remove the plastic box from the initial mounting and wrap the box in thick fireproof insulation before remounting. Also, install a fireproof shield/deflector panel horizontally below the plastic box above the opening of the fireplace. This will reduce the amount of heat that comes from the flue behind the plastic box and from the opening of the fireplace below the plastic box. However, wrapping the box in thick fireproof insulation will also significantly reduce the ability of the box to be cooled by ventilation. This means that even though the amount of heat getting to the box will be reduced, the amount of heat that can escape the box will also be reduced -- so you may still experience overheating effects if the box is exposed to heat for a long period of time.

Think about toast in an oven -- it will char black in a short time at high temperature, but it will also char black if left a longer time at a lower temperature.