I used a chest freezer/thermostat as a refrigerator for a few years. It used about 15 watts in the summer and 11 in the winter on a continuous basis (about 100 watts when running). I think the main savings was condensation, as it quickly gets to 100% humidity. Another is that the expansion coils are at the fridge temp instead of freezer temp, which should lead to a higher coefficient of performance. The top-opening door doesn't hurt, obviously. For freezing I had a fairly big chest freezer running at around 40 watts average.
I switched to a normal fridge partly due to the disadvantages (space efficiency and condensation), and partly because fridges are quite efficient these days. My old fridge of early 80's vintage used a lot of power... about 200 watts continuous, and around 700 watts when on. The chest fridge paid for itself very quickly. The new one, which is a normal no-frost top-freezer from Lowe's (not a super-efficient Sunfrost) uses 101 watts when on, and 35 watts average. I don't know why they're so dramatically different, as it's very similar other than thick doors. Thermodynamics hasn't changed in the last 30 years, but fridges sure have!
I think the best plan is to start with a modern (post-2000) fridge. A chest fridge is extremely efficient, but adding another freezer cancels it out. Robert's 680 watt draw means an older fridge and likely huge savings just for buying a newer one. The run wattage is a big deal, even if run time is up. Note that chest freezers can't be further insulated because the condensation coils are on the outside, but fan-cooled fridges don't have that limit.
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