An air gap with a small fan should give you close to room temperature on both surfaces. Kind of a DIY "air knife".
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I suppose hot ambient air on one of the six surfaces will make the fridge compressor duty cycle higher. Then you could compare your monthly savings on the elec. bill by using the barrier vs. the one time cost of materials and labor. A fridge pulls about 500W average.
One of these days I want to bring the 120v supplied to our basement fridge compressor out to a connector and run a 24 hours mech. timer.
Knowing the baseline duty cycle overnight with no door openings I should be able to tell when this old fridge begins to fail by seeing an increasing duty cycle.
We had one fridge where the door internal insulation was somehow soaking wet and this thing was gobbling power just to keep up.
You can also use this timer method to measure the heat loss from an elec. water heater. With no water usage it's about 5 minutes on for each 7 hours off.