I have a question about insulating a wall cavity. Zone 2A.

  The existing wall is about 10″ thick brick with a 1/2″ coat of plaster on the interior.
  We are building a typical 2×4, 16″ OC wood stud wall on the inside of the masonry wall. The new wall will be sheeted with 2 layers of 3/4″ MDF and painted. We can use Extira exterior MDF or regular MDF. The interior space is air conditioned.

  Do we insulate the stud wall? If so, do we use a kraft faced batt and to what side would the facing go? We can use typical fiber glass or mineral wool. Spray foam is an option as well.

  Comments are appreciated.