[Christ]

If you have an upright, one of the quickest things you can do with it, at the cost of space, is to fold up an old blanket so that it fits perfectly in the bottom area below the last shelf [typically drawer space in a fridge] and lay the blanket into that well, at least covering the odd shaped area where the compressor is usually placed.

In the case where your cooling coils are inside the walls of the unit, insulating inside it [but not outside] can still increase it's efficiency, at the cost of a little space.

If it's a really old one with the coils inside, you can also simply find out where the coils are and remove that entire panel, exposing them.