If you have a few days before bringing these items home, hang the appropriate amount of these in the storage unit (probably one or two -- but based on CUBIC feet. One will control approximately a 10x10x10 unit). If you want to target a particular box, I have heard of people putting this and the box in a large plastic bag and sealing it up for a day.
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Even with the above, be careful as BR spider bites can be very serious.