a Mike S snip...
My thinking is that honey supers will be less susceptible to SHB attacks in open storage than those supers that have frames containing bee bread and/or have been previously occupied by bee brood (pupal skins).  The honey supers won't have a source of protein for SHB larvae but the frames of bee bread and cast off larval skins would contain a source of protein.  Keep that in mind when monitoring stored supers/hive bodies.

my comments...
The sun can be very intense here in Texas during the summer months. There are lots of things that try and get themselves out of the intense sunshine during most of the day... but sadly this does not include beekeepers.  

I have found if you stack old boxes up on the edges of a hard or impervious surface that this reduces any shb problem to about zero.  Anyone who has deal with the small hive beetle for long notices pretty quickly that their reproduction and growth goes into overdrive when then hit a patch or frame of pollen.  Larval skins or honey does not seen to ramp up their reproduction like pollen so you always need to keep a watchful eye on pollen ladened comb in or out of the hive.  In terms of salvaging already modestly infested comb a quick dip in the freezer for 24 to 48 hours is the only alternative I have found to consistently work.

I don't use traps of oil to counter the shb but on smaller units (queen mating nucs) I do on occasion use swiffer duster pads to catch adults. Without a doubt the shb prefers dark places in the hive and that is where I place the pads. 

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