Time for entrance reducers?

I received this e-mail:
Hello Jim,
Strong Carniolan hive. Fumagilin fed. Small amounts of bright orange pollen still coming in. I noticed an oval area approximately 4x2 inches in the middle of one frame in the lower brood box where the bees had removed the comb completely down to the white plastic foundation. Nothing like that in the Italian hive next to it. I cannot find a reference to this on line. Problem? Thanks for the time,
My reply:
Being this is the lower brood box, a mouse has probably snuck in and chewed up a frame. Eating the honey and/or pollen.
In the lower box there are less bees in there especially if it is cool out. They are more than likely clustering in the middle box on a three high hive. They will put the run on the mice while it is warm, but when it starts getting cold the bees won't even go into the bottom box, on a three box hive. A two box hive has less of a problem with this, due to the fact the bees are in that lowest box.

Now as the cooler weather comes in, it is time to put in the entrance reducers. They should keep out the mice. This time of year I set them at the large opening.
When it is in the 70's or if the hive is being treated with Apiguard I would not put them in. But as the night time temps start getting into the 40's the mice will start to move in.