IMac (Intel) :: Fan Runs Full Speed On Shut Down

My iMac runs perfectly fine; more or less as it did when it was new. In OS X, when I shut down the computer, the fan runs at full speed indefinitely, unless I unplug it or boot back up.  When running, the fan is perfectly normal (increases speed a bit when doing something taxing).  I've never heard it at full speed before until this started happening.  After following the SMC reset procedure with no luck (I'd like to add that the SMC reset only says it relates to fan problems when the computer is ON), I searched a bit and noticed there are one or two cases where a problem like mine was believed to be a motherboard issue, and therefore a costly fix. 

However, here's the fun part. When booted into Windows 8.1, shutting down the iMac does not cause this issue to occur.  It stays silent, as it should, even if I disconnect then reconnect the power.  This leads me to believe it's unlikely to be a motherboard issue.  However I've wiped, restored, and reinstalled fresh copies of Mountain Lion, Mavericks, and Windows 8.1, and the result is still the same: if I don't want to have to unplug it from the wall, then I have to use Windows to shut it down. 

So then, my questions are these:

-What is the difference between shutting down from OS X and shutting down from Windows?

-Is an operating system allowed/able to touch BIOS settings?

-Is it possible to still be a hardware problem, given this difference? 

My default OS is OS X, and it makes no difference if I change that to Windows.  I also did a PRAM reset, even though that has nothing to do with fans...

Info:
iMac, OS X Mavericks (10.9.4)