Well if your looking to just stop the little critters from getting up
there then I would say a chimney balloon would do the trick. I use one
to keep bats from comming down my flue and I imagine it will work in
reverse.
You could go with the glass door or inserts with doors that were
mentioned but that is a pretty steep investment if you are just trying
to keep cats out. Personally i dont use my fireplace so i chose a
chimney balloon because it went in easy and kept the bats out. I do
suppose there is some energy benefit to it to though.
I suppose the DIY route may work by going with newspaper or wire
(although i just cant envision how the wire ball trick works). I
wouldnt go with the bed pilllow trick though. If some idiot lights a
fire under that you will have a smokey burnt duck smelling mess with
of without a fire blanket.