The development of chilling injury depends on the time and the storage temperature.  Link to a graph that illustrates how long it takes to see discoloration (chilling injury) on Italian sweet basil at different temperatures.  Other basil varieties may differ in their sensitivity to the storage temperatures.   Packaging (packaged product inside a carton box with additional packaging materials) will also help to minimize chilling injury at lower than recommended temperatures due to trapping the heat of respiration.   This effectively raises the product temperature.  This tactic can be used for shipments of a mix of herbs.   

-Marita Cantwell