Disclaimer: This experiment was not a success when using a plastic bucket. The principle is sound, but the impervious nature of plastic prevents enough evaporation to cool the system noticeably. If I can find a 5 gallon unglazed terracotta bucket, I will try the experiment again.
The “pot-in-pot” refrigerator dates back at least 5000 years. The principle is simple, a small pot is nested inside a larger pot, and sand is packed into the gap. The sand is kept moist at all times. When the moisture evaporates through the top (and more importantly through the sides) it cools the inner pot to a surprisingly cool 59ºF (15ºC) – cool enough to keep meat for two weeks (source)
The evaporative cooling process is the same our bodies use to cool off when we sweat.
I built one of these pot refrigerators using one of my trusty five gallon buckets, but since the only contact with air is at the top, it did not evaporate enough to make any temperature difference. We tried to speed up the evaporation by putting our fridge beside a fire, so it would benefit from the heat and dry air, but it changed very little.
We live in a very wet climate, which is bad for evaporation. The drier your locale, the better this type of fridge will work.