I am not perfectly certain but here is what I think:
1) Fire burns better under breeze because it brings in oxygen and carries the carbon dioxide away.
2) In a strong wind, the negative pressure create a vaccum sucking both oxygen as much as carbon away. (To have wind blowing, you create a low pressure zone around/near the fire.)
It has nothing to with temperature, although temperature is an intial require condition for the ignition.
(Notice how ignition is different from the process of burning. It is NOT ignition that Sherman is asking, it is burning. If the fire is already burning, is the flow of air enough to carry so much heat away to below the ignition point?)