FWIW, if it's a chest-style freezer, then there are two methods I've seen for those to shed the heat from the compressor coils. One is in a rear-mounted/under-freezer mounted setup, and the other is built into all the side and front and rear surfaces.
If it's like the latter you can't add any insulation to those surfaces while it's actually running (but you can wrap it in blankets or any other thick insulation jacket, thicker the better, after power fails to help insulate it further, as long as you be sure to remove them when power comes back on. This could add a LOT of time to keep it cold inside).
If it's made like the former, you can add on styrofoam sheets to quite a thickness to all sides without exchanger coils, whatever's practical for the area it's in, and even put insulation under and over it if it's only a rear-mounted heat exchanger. Depending on how it's mounted a rear exchanger can even be moved away from the freezer a bit and add even more insulation between it and the freezer. This can all be done and still ahve it running with the insulation on it, and it will take much less power over time to keep the stuff cold inside it.