I have the SAME problem on my 08 3.5L. And I live in Michigan so it gets pretty cold out. Just like you described, I have the 89 oct predator tuned installed and every morning for the first 2-3 seconds will make a whining/whistling noise right after start up and then it will go away when the engine comes off high cam or when I put it into reverse. Weird, I'm maybe wondering is it a vacuum leak somewhere in the intake? I have no idea, but I don't find it to be a serious problem.
There was a TSB that may be related to your issue. I could find no such bulletin for the 2011 models though. See below.
NUMBER: 18-036-08 REV. A
GROUP: Vehicle Performance
DATE: December 3, 2008
Flash: Whistle Sound From Engine Compartment/Purge Solenoid
This bulletin involves selectively erasing and reprogramming the Powertrain Control
Module (PCM) with new software and Initializing the NAG1 transmission (sales code DGJ)
or Clear the Variable Line Pressure (VLP) Counters on 42RLE equipped vehicles (sales
code DGV) with the StarSCAN®/StarMobile®.
CAUTION: It is important to initialize the NAG1 transmission (sales code DGJ) for
2008 model year or Clear the Variable Line Pressure (VLP) Counters on
42RLE equipped vehicles (sales code DGV) with the
*2008** - 2009 (LE) 300C/300 Touring (International Markets)
*2008** - 2009 (LX) 300 / Magnum / Charger
NOTE: This bulletin applies to models equipped with a 3.5L engine (sales code EGG)
built before August 26, 2008 (MDH 0826XX).
Some customers may complain of a whistle sound coming from the engine compartment
while the vehicle is running. This condition is caused by the purge solenoid. A software
change has been made to the current on the purge solenoid circuit which corrects the
If the vehicle owner complains of this issue reprogram the PCM with the new software.