This may be "totally off the wall."
Did you lap down the convex ridge of the TRUE's base to a flat copper surface?
The other remarks here are also relevant.  RealTemp has a test to indicate whether the sensors might be sticking.  I can't remember if you mentioned that.
The sensors may be crap, and per Intel's own admission.  But there was another angle on the issue:  Look for a March, 08 Anandtech article about how sensors are read and interpreted -- it dealt with the E8500 Wolfdale.
My 680i motherboard is in the sunset of its lifecycle, but ASUS had forward vision toward making it Penryn-compatible when the processors were finally released.  In September, 07, they posted a revised BIOS -- more likely to accommodate the G0 steppings of the Conroe.  Later they went through two more BIOS revisions coming into March of this year.  The first of them would recognize my E8400, but the idle temperatures as shown in BIOS monitor were way too high, or 50C degrees.  The earlier BIOS showed them at 10C, which was ridiculous under a room-ambient between 20 and 30.  
They finally posted another BIOS revision in first week of this month, August 2008.  Suddenly, all the core values and tCase values seem spot-on, even if they didn't list a fix for this in their BIOS-revision "fix-list."
The Wolfdales, if I remember the Anandtech article correctly, implemented a different approach to the sensors and their interpretation against tJunction.  So older BIOS revisions would have trouble with it.
When did you buy that Gigabyte (P35 chipset?) motherboard, which BIOS revision does it have, and when was that BIOS released?
Lap the TRUE anyway -- if you want to take the time.  The trick to it:  clamp two metal or wood blocks to the sides of the base so they meet the sandpaper level with the convex ridge of the base.  Once you see a flat surface along the ridge, you can dump the clamp and blocks.  The ridge on the TRUE's base accounts for less than a millimeter's difference between the base before lapping and after lapping.