Refrigerator is the heat machine which produce cold, and thus the following thermodynamic principle applies "the coolest is the cool source (back of the refrigerator), the better is the performance of heat machine".
The installed capacity of a typical modern refrigerator is 200 W. However, the refrigerator's operation is cycle-based, meaning it spends 25% of the time cooling down, and when it reaches the right temperature, it stops cooling until the next cycle. Therefore, the average is 50 W or about 1 kWh/day, and 365 kWh/year.
According to thermodynamic cycle, per 1 degree Celsius decrease dQ=1 W (peak capacity reducing due to measure (or 0.25 W of average daily/annual capacity)).
Let's suppose that dT=10 0C for 6 hours/day (representing the sunny day and/or other heat source which works periodically). Then, for this period 6 hours/day, peak capacity will be decreased on 10 W (190 W opposite to 200 W) and average daily will be decreased to 37.5 W opposite to 40 W. For other 18 hours per day it remains the same (200 peak and 40 average). Then, for the daily average it will be 960 Wh (w/o measure) against 945 Wh (after to measure) . The difference is 15 Wh/day. For the year it will be 5.5 kWh.
No investments, just creating a saving habit.