I've never done it before, but I've heard if you use sheets of the foam insulation and sandwich a few of those between plywood for each wall, it proves to be very effective at holding a temperature and then you can use something very small to cool it and it will stay cold for a long time.
^^That's how I've always seen it done.............^^
Insulate the top bottom and sides and a smallwindow air conditioner will do the trick.