There is a lot of false information out there in regards to the energy efficiency of the refrigerators from the 30's, 40's, 50's and early 60's.
They are more energy efficient than you think. It wasn't until the later 60's when the appliance makers added the automatic defrost feature that they grew more inefficient. They also tried making the cabinets larger by making the walls thinner.
I currently have two old frigs, both are new to me in the last couple weeks. I have one plugged in right now to a Kill A Wattmeter, these tell you how much energy is flowing through the meter. My 1935 GE Monitor Top frig uses 0.42 kWH per day. Granted my garage is cool right now and it is not running as much as it will be this summer. My current electric rate is 7.5 cents per KWH, right now I am paying $1.00 a month and this summer I will be paying about $2.00 per month for the frig.
This frig has about 3.5 inches of insulation, sandwiched by steel. They literally are ice boxes and they weigh about 500 pounds. The ones from the 50's are lighter and nicer to look at with the curves.
The second frig I have is an IH from 1952. I have yet to plug it in. I hauled it on its side and need to let it settle for a few days.
Don't believe what you read about energy efficiency and old appliances.