There is no single answer, because the question hides three different products with three different physics. Ask it separately for frozen, for fresh raw material and for dried.
Frozen finished product
The controlling requirement is a deep-frozen chain held stable through storage, loading, transit and delivery, verified with calibrated loggers. The number matters less than the stability: repeated small excursions do more cumulative damage than one brief deeper one, because each partial thaw and refreeze grows ice crystals, ruptures more cells and drives moisture migration that shows up as freezer burn and block formation. The relevant framework for international road transport of perishables is the ATP agreement, and the operational discipline is set out in the cold chain management guide.
Fresh potato before processing
This is where the interesting trade-off sits. Store too warm and the crop sprouts, respires and loses weight. Store too cold and cold sweetening converts starch to reducing sugars, which then darken during frying and drive acrylamide formation. The correct set point is variety-specific and end-use-specific: a crop destined for fries is held warmer than a crop destined for a cooked or dried product, and it is monitored by periodic sugar screening rather than by temperature alone. Codex CXC 67 describes this control set as part of acrylamide reduction practice.
Before any of that, the crop needs curing – a short warm, humid period after lifting that heals wounds and sets the skin. Skipping it guarantees storage losses regardless of how well the store is run.
Fresh carrot, parsnip and other roots
These are held cold and very humid, close to but above their freezing point, because they lose water quickly and go limp. In an export processing context the practical answer is usually to shorten storage rather than optimise it: freeze or dry close to lifting and accept a concentrated campaign.
Dried and dehydrated product
Temperature is secondary. The governing parameter is water activity, controlled by a moisture barrier pack rather than by a chilled room. Store ambient, dry, away from strong odours and out of direct light, and protect the pack integrity – a compromised liner will undo a correct drying specification within weeks. The processing and storage guide covers all three cases in more detail.