Yes, potatoes can be stored at 40°F (4.4°C), and it's actually within the recommended temperature range for certain uses, though the specific temperature choice depends on the intended purpose.
According to USDA and university extension guidelines, fresh market/table stock potatoes should be stored at 3-6°C (37-43°F) with 90-95% relative humidity. At 40°F, you're right in the middle of this optimal range for fresh consumption potatoes. This temperature effectively suppresses sprouting and respiration while maintaining quality for 4-8 months depending on variety.
For seed potatoes, the recommended storage temperature is slightly cooler at 2-4°C (36-39°F) according to FAO and CIP guidelines, so 40°F would be at the upper end but still acceptable for seed storage applications.
However, if you're storing potatoes intended for chip or french fry processing, 40°F is too cold. Processing potatoes should be stored at 7-10°C (45-50°F) to prevent "cold sweetening" - the conversion of starch to reducing sugars that occurs below 6°C. These sugars cause Maillard browning during frying, producing dark-colored, bitter products and potentially harmful acrylamide formation.
The key is matching storage temperature to end use: 40°F works well for fresh market potatoes but is problematic for processing varieties destined for frying applications.